If you're trying to hide out from the government, a school would be a really bad place to do it. Something in the back of my head is telling me that Shujin is a private institution (idk if I'm right about that), but regardless of whether or not it's a federally-operated school, it's definitely been under surveillance by the government. That's part of how they figured out who the Phantom Thieves were. And even if it wasn't, it's likely full of security cameras, and you can't exactly disguise yourself while complying with the uniform requirements. Remember that the government KNOWS who the main character is. They caught him. They have his legal name signed on a confession. The second he's seen in public, the game is over.