I think we need a better mechanic for allowing characters to react to things that aren't on their turn. Something universal that options can be attached to and that doesn't require careful attention.
For a quick example, let's say that each round, each character has one move, one action, and one reaction. On their turn, they may take a move and an action. They may also make one reaction at any point during another character's turn.
Most reactions would probably be defensive: Setting a pike against a charge, taking a defensive stance, casting a ward. Once chosen, you can't change it until your next turn, and you can't make any more reactions.
Opportunity attacks would also be reactions. They don't need specific triggers. Whenever someone you threaten does anything, you can use your reaction to attack them. If it's a spell, you might disrupt that spell.
Of course, such a system means a lot of off turn actions, but they're never "gotchas!", and it would give everyone at the table a reason to be paying attention to the battle.
Regardless, it's just an example of a unified mechanic. I'm sure someone can come up with something else.