I may be missing something here but why does it look like nobody in Rabanastre (or anywhere else) seems to recognize Ashe?
I assume as princess she was mostly kept out of the public.... Vaan mentions that early on... That he barely even knew there was a prince and that he didn't even recognize her up close. So other than her wedding, maybe she rarely appeared in public, or at least not up close.
Even Balthier, ever observant, may not of... I was never all that sure if he knew. Same with Larsa. When he first meets Ashe, it seems like that one scene where he tries to stop her from going after Vayne (after the fire horse fight), it felt like maybe he stopped her in a knowing way... more than just protecting a resistance girl but maybe that he understood it was Ashe. But on the Leviathan he seemed pretty surprised, too.
Then, same with Larsa... Which was weird, too, for him not to notice. But when Larsa first acts to join near the aerodome and the guards run by, Balthier seems to let him join because he sees he's hiding from the guards; I thought he recognized him as Larsa or at least royalty, but in the mine (right before Ba'Gammon) he does seems to not know who he is until he sees him rejoin Judge Ghis.
So I sort of figured, maybe he recognized both as being obviously more than who they were: maybe, respectively, not just a fighter but an important Resistance leader; and not just some kid but obviously some sort of Arcades royalty (the type that would have a Sandalwood Chop haha), but in neither case knowing precisely who they were.