Mmm... this question comes across as really, really bad faith.
But to engage with your question in good faith, despite said question being in unquestionably bad faith, people have brought up a lot of things which I broadly agree upon. The clans are one thing that's unquestionably BattleTech, their particular flavour of technobarbarism aren't something I've really seen elsewhere. Sure there's "proud warrior race guys" in many if not most sci-fi properties, but the eugenics program, bloodnames and all that seem pretty unique and specific. I like looking at fictional settings and imagined societies and seeing what people come up with, and the clans are by far the most creative imagined society in BattleTech, which unfortunately is not really that difficult considering the other ones, but I think they'd stand out fairly well even in more outlandish settings.
I think also, there's an aspect which I don't seem to have observed in other posts which I think bears consideration: the clans just have better branding.
I mean, look at them: Clan Wolf! Jade Falcon! Ghost Bear! Smoke Jaguar! These might sound unspeakably over the top to you, but they sound like the names of a sports team or mascot, which isn't too far from what they really are. Their logos are comparatively straightforward and simple compared to other factions, mostly 'animal on semi-abstract background', compared to, say, the excessively busy Federated Suns logo that for many, many years I never even realised included a sword because it's just got so many lines and points and stuff. I can see people wearing bright green Jade Falcon sports jackets with the logo and all and seeming pretty cool compared to, say, green Capellan Confederation jackets with the triangle even though they both have the cringey katana. The iconography, naming and such are just plain cooler than the other factions.
Compare this to the great houses: Federated Suns, Capellan Confederation, Free Worlds League, Lyran Commonwealth, Draconis Combine. If you knew nothing about the franchise, would Federated Suns, Capellan Commonwealth and Lyran Confederation sound meaningfully distinct to you? They all sound similarly mealy-mouthed 'good republic' to me, even though none of them are, and I even mixed up the CC and LC because they're so damn anodyne. Sure, Wolf doesn't have much inherent meaning compared to Jade Falcon, but they're meaningfully distinctive and easy to tell apart.
Of all the great houses, the Combine easily has the best branding: 'Draconis' means dragon and sounds cool and badass, and 'Combine' is a rare enough noun for a faction that it sticks out. They're also bright red and have that dragon in circle logo which is so cool Mortal Kombat basically uses it for their logo too, and that's before we get to all the katanas and Japanese and samurai stuff which sticks out from the vaguely western/European melange that comprise 60% of the great houses.
The Free Worlds League could, on name alone, be decent branding, and they've also go the eagle, which has been a pretty clear winner in terms of iconography for literally thousands of years. If they separated out that purple into red, white and blue they'd pretty clearly be your 'Murica stand-in and the obvious 'good guys' of the setting, so of course they're vaguely based on the Austro-Hungarian empire largely ignored for something like thirty years of real life history. If the game setup was the scrappy, freedom-lovin' patriots of the Free Worlds League against the evil, militaristic black and red empire of the Draconis Combine, it would slide much more easily into the cognitive space most people have in their heads. Generic, yes, but honestly it's a lot simpler to understand and pick a side than trying to explain that, see, the Federated Suns is Anglo-French European, the Lyran Commonwealth is Germanic European, and the Free Worlds League is 'hodgepodge of vaguely ethnic, not well known/understood central and eastern' European, and that's how they're different.
Compare that to the 'independent, innovative Wolves', versus the 'proud, rigid Jade Falcons' and 'vicious, savage and aggressive Smoke Jaguars' and you get the idea of who stands for what a whole lot quicker, especially as, at least at one point, they really did stand for different things, whereas the great houses largely stand for which feudal dynasty gets to rule the galaxy. Yes, there's substantial variation in what precise blend of despotism this means, but that's all this complicated nuance stuff that threatens to bore people off the whole setting if you're not careful about it.
I confess, I'm one of the people who first learned about BattleTech with MechWarrior 2 and the Wolves versus Falcons, so they were my introduction to the setting, but when I went to my local library and found the tie-in novels, I struggled to tell apart the different IS factions. I didn't realise, at any point in the novels that Victor Steiner-Davion was from a different nation state than Kai Allard-Liao; there's a good argument to be made that the St. Ives Compact wasn't really an independent nation state of its own, but all I saw was the broad brush of 'Clans vs. Inner Sphere', and while I could distinguish the different clans, because of their simple names and broad themes, the only great house I could recognise as distinct from the others was the Combine, because, as I mentioned above, they have by far the best branding.
My vague, half-remembered scraps of the cartoon conflated the 2nd Star League with the Federated Commonwealth (what a generic name!), which MechCommander, MechWarrior 3 and 4 entirely failed to disabuse me of, and I only really started 'getting' they were different in MechWarrior 4 Mercenaries when the FCCW was the main event. Frankly, without a grounding in the 3025 status quo, how was I supposed to tell apart these two western European flavours of feudal despotism, that they weren't 'naturally' the same faction? You have your blue western European kingdom fighting your yellow western European kingdom. Very distinctive. Sure, the blue guys are the bad guys, but nothing really communicated to me what, aside from their moral alignment, makes them different to the yellow guys.
Aside from the Combine, of course, there are actually factions in the Inner Sphere that are fairly distinctive and have good branding, but these aren't actually the main nation state players: most of the higher visibility mercenary units had decent branding, which I suppose is reasonable, given that branding is an in-universe concern for them as well. Wolf's Dragoons! Kell Hounds! Gray Death Legion! Incidentally, all of these things also have simple logos that would look good thrown on a jacket or t-shirt, though the names are perhaps less descriptive than the clans, who conveniently actively ape their namesakes in behaviour, but they at least sound cooler than the leaden, political names of the houses.
ComStar and the Word of Blake should have had good branding as well, what with the otherwise unused religious imagery, unique organisation, distinctive worldview, clear iconography, except that on the whole ComStar never really did anything involving giant robots blasting each other except Tukkayyid, while the Word of Blake were saddled with, well, the name of Word of Blake. Who is this Blake guy, and what's with this 'Word' of his? Red robes, cyborgs, superweapons and broadsword imagery weren't enough to save them from this spectacularly uninspiring name. They had all this crazy, techno-messianic-apocalyptic madness hidden behind that painfully dull name, and I guess it hardly helped when their one big shindig only happened in confusing retrospective sourcebooks.
It's quite telling that, in MechWarrior Dark Age, with the little splinter factions fighting amongst themselves, those factions were named something much more distinctive than their parents: 'Swordsworn', 'Dragon's Fury', 'Stormhammers'. Honestly, Dragon's Fury is pretty unnecessary for the best-branded great house, but sure. I don't know how the 'Federated Suns' is supposed to be meaningfully different from the 'Lyran Commonwealth' on names alone, but Swordsworn and Stormhammers give me some ideas as to how they're different while being largely true to the greater factional stereotypes. Honestly, I'd have had the Stormhammers named something about a fist instead, given hammers aren't a big part of Lyran iconography, but in getting across the idea of the faction (heavy hitting, brute force, no subtlety) it does the job pretty well.
To go off on an entirely different tangent, one thing I find fascinating about the clans is this attempt to be what I'd perhaps describe as a 'constitutional kratocracy', which isn't a concept I really find in other settings, though maybe if I was a die-hard Trekkie or Star Wars nerd I could make useful comparisons to Klingons or Mandalorians or whatever. In most of your 'proud warrior race guy' societies, you can overturn things with a duel to the death, sure, but aside from vague allusions to 'traditions' there usually aren't really any constraints on those challenges and duels. I find the clans particularly interesting in that they take this incredibly pessimistic view of human nature, i.e. that at the end of the day if someone really wants something he'll use deadly violence to get it, and, seeing it as inevitable, rather than trying to outlaw it, instead create a legal process to fit it into how society works without collapsing into anarchy.
Yeah sure, you can disagree with what your superior officer and throw down with him over it, but there's a whole bunch of procedures you go through if you want to go that far. Okay, you can try to overturn a majority democratic vote with force of arms, but the forces in that fight are in direct proportion to the final count of votes. Absolutely, if you really don't like something, you can use violence to protest it, but there's a time and a place for that we all agreed to; we're not savages, we're civilised warriors, and you can't just go around killing people you don't like at the drop of a hat, that's just barbaric.
This system of course falls apart in the Wars of Reaving, but, to me, it's an unusually well-elucidated system with its failures and weaknesses well-examined, at least partially to appease not-entirely-good-faith Inner Sphere fans with a hate-on for the clans after the terrible balancing of their introduction, but the setting is richer for it.
Comparatively, most of the Inner Sphere societies aren't subject to nearly the same level of scrutiny, probably because they aren't subject to nearly the same level of imagination in their creation, largely being 'like reality except politics is all aristocratic and feudal', or in the Combine's case, a particularly horrible aspects of various eras of Japan. The only one that has at least some imagination is the CapCon, which, for its sins, is the most aggressively interrogated of all the Inner Sphere societies by the fanbase. I won't really go into it here, but unlike at least some other states, it doesn't just seek to ape its historical antecedent but come up with its own vision and philosophy of totalitarianism; if the CC was just some ugly caricature of imperial China, it'd probably get less criticism from the fans.
I think, aside from being overpowered in their initial introduction to the game, the clans also have a certain amount of cachet as the 'high tech' faction, and if you stripped away all of their technology they'd lose something, but I don't think their unique technology needed to be overpowered, merely 'high tech' to retain that cachet. If the clans just had X-pulse lasers instead of their superlative clan versions for example, rather than the crappy, 2/3 range Star League versions the Inner Sphere were stuck with, that might have been enough to maintain that technological mystique, even though nobody thinks X-pulse lasers are overpowered.
Of course, if that were the case we'd probably have people shrieking about how X-pulse lasers are obviously, gruesomely overpowered and it's totally unfair these stupid clans get them, and extremely poorly veiled insinuations that it's only because they have such things that people like the clans.
