An AST is a tree as much as the directory structure currently encoded in git.

It shouldn't be hard to build a bijective mapping between a file system and AST.

Right, but for what purpose? I don't see much gain, and now you're left trying to fit a square peg into a round hole. The git CLI would be technically working, but not practically useful. Same with an IDE: if you checked the files out you could technically open them but not easily change your program.