I think some of you are jumping the gun in asserting that the matter of the Khanship of the Falcons is "settled". These are the Clans, and we've seen them devour and genocide each other over far less pressing things than an illegitimate Khan...and yes, by Clan law, Jiyi Chistu is 100% illegitimate; he was not voted into his position by a quorum of the Clan's Bloodnamed warriors. Hell, the Falcons just fought a civil war over the legitimacy of their Khan within the last twenty years, so it's not like there isn't a precedent here. WoR showed us that the Clans are big on the letter of the law as much as the spirit (hence why it took them so long to overturn the Great Refusal), and the Falcons are one of the most conservative Clans that ever existed.
While I do agree that 1) current circumstances prevent Alaric and Stephanie from dealing with that situation right now and 2) the expression "possession is 9/10ths of the law" absolutely applies here right now, it seems rather foolish to assume that there won't be a reckoning at some point. Especially with Alaric in the mix; we all literally just watched him demand the RasDom go all-in on his new Star League, and we've seen the lengths he will go to in order to get what he wants. And if that so happens to be a united Clan Jade Falcon, well... a reckoning will happen sooner or later.
Then, of course, there's the biggest reason why the Khanship of the Jade Falcons is far from "settled": this isn't PeaceTech, it's BattleTech, and we've watched factions make foolish decisions time and time and time again because those decisions fuel the incessant warfare that makes this setting what it is. If TPTB decide that Alaric and/or the Terran Falcons decide that it's time to bring the rest of the Falcons under the new Star League's aegis with the Khan that actually was elected by her Clan's Bloodnamed warriors, then that's what we're gonna get.
Opinions are all fine and dandy, but let's not speak of them as if they're facts. No one here knows how this story is going to go.