Your first statement...could use some proof, but I'll certainly concede that D&D isn't perfectly balanced.
I'm not sure what kind of proof would satisfy folks.
But I think we could start by trying to agree on what "broken" looks like. In my opinion, it's probably something like this:
1. Does the game completely lack challenge?
2. Is the game basically impossible?
If we can answer either of those with "yes," then the game is probably broken in terms of balance. Otherwise, as long as there's challenge, but things are still winnable, then we're more than likely safe.
Now. Imagine that everyone had unlimited attacks of opportunity. How would that break the game?
If anything, players would just have to be more careful about moving around on the map. Maybe some folks would be more inclined to choose a feat or magic item that allowed them to avoid opportunity attacks.
In no way would it break the game. Opponents would still have to roll to hit, etc. As it is, I rarely if ever get hit with an opportunity attack because I avoid them.
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The only reasonable argument I can think of that's an issue is the loss of spell slots because of they way Counterspell works.
Which I have suggested changing.
