The flip side of a proof assistant's 'minutiae' (and there's plenty of room to disagree wrt. whether paying attention to those minutiae helps with gaining a better, more accurate intuition!) is its ease of refactoring a proof. A proof assistant can instantly tell you whether a seemingly nicer, better-abstracted proof B really manages to prove the same thing as proof A, something that's very hard to do without the use of precise formalized statements and automated checking.