While I groaned on the whole
Easy Amnesia trope being applied to Yotsuyu, it's what we have to deal with, so let's run with it: It's a mistake to think of it as Yotsuyu getting off scott-free. She WAS punished. She DIED. More than that, she died in despair, because she didn't get the satisfaction of taking Hien with her, and died knowing it.
Assuming that the amnesia is permanent, justice has already been meted out. The problem is that, as a side effect of Yotsuyu's death, a new woman - a child, really - named Tsuyu had the misfortune of being born into the woman's body. If we accept that the amnesia is real and permanent, then there is no obligation to punish Tsuyu for the crimes of another woman, especially since that woman already paid for those crimes with her life.
The folks Yotsuyu hurt already have their closure; as far as they know, their tormentor died in the castle collapse. Seeing a woman wandering around with Yotsuyu's face would certainly reopen those wounds, but there's no need for that to happen - just exile her. Get her out of Orthard, let her live out her days in Eorzea or something. Of course, a complication arises in how attached she is to Goetetsu, who'd be reluctant to leave his homeland permanently, but he's accepted responsibility for her and will do what he needs to do - even if that means staying with Tsuyu until she's confident enough to stand on her own.
All that said, though, I think it's pretty likely nothing's going to be as neat and tidy as all that. I think the odds are strong that Tsuyu will regain her memories of being Yotsuyu. The question of what to do with her could then become a whole lot more murky - especially if she's horrified and genuinely remorseful of her past self's dark deeds.