Why should he have stuck around?
Let me count the ways:
1) Because this is almighty governmental cluster foxtrot and he damn well owns a chunk of it.
2) As a senator he has the juice to get things done/needed/acquired and is in a far better position to do it if he’s close enough to get in someone’s grill.
3) Optics do matter and bugging out looks as bad as it is.
4) You don’t learn from your mistakes by running away from them.