CubicsRube
Hero
I'm of two minds about this.They would need to give standing up a meaningful cost. using half the movement you weren't going to use after getting knocked down in a melee combat has no impact on the game. standing up provoking an AoO was removed in the name of streamlining/simplifying just to simplify so the cost/benefit of things that trigger prone or allow standing up at a different cost are messed up since few if any of them were improved in other ways to offset the loss/gain.
I do think that a few items like picking up a disarmed weapon on the ground and getting up should provoke attacks of opportunity, but I'm leery of having 3e levels of AoO triggers to remember. There's a level when it gets too much. However for a few things like that it should be ok.
I do worry however that an AoO on prone could be a real death spiral for PCs. If they get knocked prone and swarmed by a group of enemies then their choices are that all attacks next round have advantage on them, or they eat a ton of AoOs. I'm sure it's realistic, but I'm not sure it would be fun at the table.