as a dedicated clan player, most of the time it feels like a good 60% of the vocal fanbase dislikes the clans. I would probably have never gotten into the game to the depth I have without them though.
I like their technology. the clans, and the things innovated by the inner sphere in response to the arrival of the clans make games go faster. I have more fun and get more options by way of their inclusion. it is markedly not the same game as one plays in 3025, and whether that's a good thing or a bad thing is personal opinion. It's not even a munchkin thing really, I don't mind if everyone has access to the technology. I think the inner sphere should have been replicating invasion era clantech by the start of the jihad really.
I like warrior cultures. the clans are bands of Warriors and not Soldiers, and I find it far more enjoyable to play an exceptional warrior character, out for personal strength and glory as much as the success of his tribe, than I do an unremarkable soldier, whose strength is entirely a function of the whole. I also like the "High Tech, High Skilled, Highly Outnumbered" aspect of the clans. I like it in the clans, I like it in other media too. the clans have nothing on most gundam shows' tech/numbers gap, for example.
I like that the Clans have an unusual culture, that their norms and values are rearranged by the experiment that bore them. The clan system being what it is, means an individual warrior need not fear death so much, knowing that his legacy continuing is not wholly dependent on his survival. I love their system of Trials, it's a great way to facilitate small unit actions without stunting the growth of the world around them. You're fighting five on five because that's all the objective in question is worth, not because five mechs is all you could get ahold of.
Battletech is also a game about fighting. Warrior Cultures and their obsession with points of honor and conduct are WONDERFUL for providing excuses to fight, and with the Trials in the clans, you are never lacking for a reason to have a battle. You are having this duel because of this unforgivable slight to your honor. or to refuse the outcome of a political decision, or for possession of that mcguffin over there. You can constantly fight, but do not have to do so at the fever pitch of all-out-war.
Really, there's very little functional difference between the way of the clans and the way of the succession wars when you really look at it. You say objective raid, I say trial of possession. You say retalliation strike, I say trial of grievance. You might find the trappings a little goofy if you're not into them the way I am, but they're tracing the same path.
I like the clan rank system, it's very straightforward.
I like the clan organizational systems. With the different definitions of what constitutes a "Point" in a star, you can do some very interesting things in playing around with unit composition. If by the fluff I'm going to be forced to adopt combined arms, I may as well get something out of that.