Red's rant: Serious question: is Uchi an exhibitionist or just naive?
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Ushi is not an exhibitionist, she's a child. A young teenager, more specifically, as she met Kiichi Hogen when she was like 11 and "Ushiwakamaru" is the name she took up after that whole thing.
That said, given the fact that per FGO she does not actually understand the concept of love, and also per FGO she seduced Hogen's daughter during that whole thing, it's entirely possible that she doesn't realize why said daughter gave her access to all the secrets she was going to eventually learn under Kiichi Hogen's tutelage and is just wearing that outfit still because she thinks it's lucky or something.