BookTenTiger
Sad Dad of the Revolution
If you want to make Opportunity Attacks more tactically interesting (which is to say, "more fun"), you could bring back some of the triggers from 3.X and Pathfinder. Casting a spell, drinking a potion, lighting a torch, loading a crossbow, standing up from prone...there was quite a long list of things that could provoke OAs besides "leaving a threatened square." That could really mix things up.
If you go that route, you might want to add ways to avoid them also. The Crossbow Master feat would let you load a crossbow without risking an OA, and the War Caster feat could let you load a crossbow without risking an OA, for example. Maybe you could spend all your movement to stand up from prone to avoid an OA, or maybe the Athlete feat could let you stand up from prone without risking an OA at all. Etc etc.
Now that I think about it, this sounds like something that would fit nicely into the ""What features should a Advanced 5th Edition have"" thread: more ways to provoke (and negate) opportunity attacks.
I think this is an interesting idea. However, again, I don't necessarily want to discourage my players from taking actions like lighting a torch, loading a crossbow...
(Man, I had that list memorized back in my d20 days!)
I do think it's interesting that 5e limited Attacks of Opportunity to only leaving a creature's reach, and made it a reaction, which means some character builds will never want to waste their reaction on an AoO. It shows that it's actually a small part of combat.
For whatever reason though, at my table it really discourages my players from moving around the battlefield, which is something I find fun and engaging.