But he did fall, to Clan Lok (or a rando pseudo-imperial bounty hunter) at that, and the rest of the clans re-assimilated under the Vindicated's flag without question before he was even dead. Literally the only one still fighting was Jicoln, and every Mandalorian down to his own son was willing to take his head.
As for the mandos ever leaning towards the Republic, why? The only time Shae has worked with the Republic is with the Alliance and the coalition, both times are only because the PC is involved. And if we want to go meta reasoning, what would you tell Mando BH's? "lol sorry but your guys just decided to swap teams :^)"? That's ridiculous. They're tied to the Empire for the rest of SWTOR just by virtue of being a core component of an Imperial class.