I think people are to hung up on what IlClan used to mean and letting that cloud their judgement.
I agree totally with this. The previous definition of ilClan is only a Revival-era concept. You get the clan flagship (no longer available), ownership of katyusha city (no longer available), your clan permanently gets ownership of the ilKhan, and the non-clan-specific bureaucracy and staff are managed by you. That's it, IIRC.
And it's not at all clear that ilKhan is anything at all other than an out-of-date incentive from the original invasion. And to the extent that it exists at all, it might well have been refused along with the rest of the invasion in the Great Refusal.
I think everyone is assuming that becoming the ilClan is going to be the end of the story. To me, I see the title and think to myself, "A clan wins Terra and declares itself the ilClan. This is the story of what happened next." At least, that's how I'd write it. And what's important isn't how the politics would work out in some poly-sci theoretical sense, it's what will make for an interesting and fun game, and what makes sense from a writing/game development standpoint.
With the Wolves or Falcons, it's clearly a setup for extermination or at least being seriously taken down. But other than thinning out the supply of Wolf remnants, there aren't really any clans left that I want to see eliminated. Though they might see things differently. That could be how it plays if it were the Wolves-in-Exile or Nova Cats, but I think it could also be written as a massive surkairede story where this becomes the premise for one of them returning to the Council of (Seven). The Ghost Bears and Snow Ravens aren't interested IMO. The Home Clans would be an interesting twist, and a very interesting way to set up for the time jump.
Two other possibilities. First, the Sea Foxes. They're the only ones who would
care about running the inter-clan bureaucracy. With strong mercantile ties to the rest of the Inner Sphere by this point, they're also the only clan that could take Terra where the other factions would have at least some excuse to accept their suzerainty. It would be much like ComStar: a pseudo-corporate neutral third party that isn't itself a major threat to the Inner Sphere. It's a stretch, but a writer could set up the right preamble to have it make sense, and you could have several interesting options for an aftermath that is interesting and gamer-friendly.
The second possibility is the Goliath Scorpions. They're a clan in between, literally and figuratively. They're also totally on their own, isolated from the Grand Council and the Council of Six, fit only to be used as pawns in the espionage proxy war between the respective factions' Watches. So a "hell bent for leather" attempt to reforge the Star League by collecting the ultimate fragment of the lost Star League -- Terra -- might be a play of desperation rather than play for power. (And again winning terra for the clans might be offered as Surkairede to get back into the good graces of the IS clans). Suddenly the Scorpion Empire becomes a legit clan again. Sure beats forming a Council of Three with the exile wolves and cats.
Anyway, ultimately you still want a fragmented IS with room and motivation for Mechs to fight one another.