BookTenTiger
He / Him
2) It might open new strategic option via positioning, but you'd rob your players of some of the existing strategic options that revolve around AoO, like the PC with high hp and AC provoking the enemy's AoO and force it to use its reaction, using the protection fighting style to shield another from an AoO, teleporting an ally out of AoO's reach, using spells like fog cloud to impose disadvantage on AoO, etc.
3) In D&D, PCs have little reasons to move in general. In mind's eye, it's easier to imagine combat as a fluid entity but on the square grid, there is no point of going places other than flying to the rescue of another player or moving out of a spell's area of effect. If PCs can do that without risks, it cheapens the "drama" of the situation.
4) What one consider fun strategic option, or out-of-the-box thinking, another may call it abuse or cheesy shenanigan, and at a point the trick gets more tiring than fun. Potential AoO are already the gambling elements of many strategies; I'm not sure if removing that gambling element would be wise.
However, I think a middle-ground could be reached if you decide that "mooks" monsters and creatures don't have a reaction, while "normal" creatures do. PCs are fighting 15 goblins, a goblin chief, and an ogre, perhaps only the chief and the ogre can deliver AoO. But even then, potential AoO is sometimes the only real threat of numerous, low CR creatures, so IDK.
I think these are some really interesting ideas!
Some of these posts are really making me think about how to incentivise movement.
I'm still having fun imagining replacements for enemy AoO. How about something like this for some enemies:
Blast
As a reaction to taking damage, the creature creates a 5 foot zone of blasting energy. A creature starting their turn in the zone takes 1d6 (fire, thunder, cold, etc) damage. The zone vanished once it deals damage, or at the start of the creature's next turn.