It is worth noting that, while the Snow Ravens are the dominant power in the Raven Alliance, they saw fit to leave the office of Alliance President in place. Not least since, unlike in the Rasalhague Dominion, the Raven population for the most part keeps to its separate enclaves, leaving the bulk of the Outworlder populace to its own devices. Even the AMC still exists, with its Inner Sphere regimental organization left intact - albeit serving very much as a second-line force when compared to the Snow Raven touman.
While out in the Scorpion Empire, the rise of zarKhan Emmy Line - an ex-Hansa freeborn, now the head of the Empire's civilian government - shows that Clan Goliath Scorpion is willing to chart its own course, in terms of how it balances its military and civilian needs going forward.
So there is plenty of precedent, should Alaric (or one of his successors as ilKhan) look for ways through which to give the population of Terra a meaningful stake in the new Star League - and, by extension, to free up more of his touman's resources towards fighting his external enemies.
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In terms of logos, I think of how the Scorpions took elements from both the Imperio logo and that of the now-former Hanseatic League in order to (re-)brand the Scorpion Empire.
Similarly, perhaps Alaric (or, again, one of his successors) might brand a new Terran realm, by taking the Clan daggerstar and merging it with elements of the Republic of the Sphere logo.
Now, where might I have seen such a logo before, I wonder...