I understand that messing with the action economy can lead to game-breaking results if you're not careful.

Let me remind you that Tunnel Fighter was a thing, and actually made it into print in the form of the 18th level Cavalier feature in XGtE. Granted, it could only be used for OAs, but allowing infinite of any type of action surely has to be much worse than what I'm proposing.

Haste and Action Surge also exist as precedents for allowing a character to take two actions rather than one. Reactions are substantially less useful than actions, and in particular can very rarely be used without something else triggering it. Meaning, often you won't be using even one reaction every round.

I'll admit, I can probably tune the feat down, but I don't think one additional reaction is quite as strong as you make it out to be, though it's certainly a handy thing to have when you have a lot of reaction abilities.