Yeah sure probably. It's mostly compatible and there are few neat new features added to some of the classes. If have a gripe it's some subclass levels being moved but that's about it. To be honest, it would be weird to continue to play 3e when 3.5 came out and added a bunch of new content and rules, and I feel the same way about going from 5e to 5.5 or whatever. Most arguments I see against switching over are literal pedantry, misleading, or could be solved by moving a singular digit.
This. DM's aren't really in charge of keeping track of them. Most of the effects are player tracked (vex, nick), a normal effect (toppling), or happen immediately (cleave, graze). If your fighter player can't do the first, and you're not interested in tracking normal conditions in the games, there is always something easy like the latter effects.