Honestly, nothing. The battle system would have to undergo a fairly large revamp for PvP to work. If it were to be implemented in its current state, it'd be a disaster. The optimal strategy would be dodge as much as possible, rendering any moderately slow quick moves useless. Also, there would have to be some kind of incentive to battle, it'd get boring within weeks. Similar to raids - I'm sure many, many people would've stopped caring for them as much (excluding Legends) if raid-exclusive rewards weren't a thing.
Of course, as mentioned, rewards for something that should be accessible at any time would be a tough nut to crack. All of these predicaments lead me to hope PvP isn't going to be a thing for a very, very long time - potentially, ever. After all, Niantic is pushing PoGo to be a team game, not a competitive 1v1 one. The main series Pokemon games are where the battling should remain.