I notice no one has bothered arguing why unlimited reactions are bad.
First off just making the reaction system in play unlimited doesn't address player's concerns about being able to pick and choose how and when they get to use certain limited resources other then just the reactions themselves.
It doesn't have to be full on pop-ups every action that occurs, I've seen some other suggestions that might work, but I'd personally like the reaction system to move more to that level of control for the players.
That said, unlimited reactions itself would remove some strategic/tactical options from game play, which I personally would like to see more depth put into not less.
Then as others have said, there are some cascading effects that could create seriously annoying situations. Add Sentinel polearm fighter in hallway/choke point to those others have mentioned. Nobody could get past it or within melee range even if not using a reach weapon. Misty step would work to get past to that fighters buddies behind but I think that is it. I'm fairly certain since BG3 doesn't do a real z axis, an attempt to jump past the fighter would still result stuck and unable to move right at the edge of their reach.
PLUS unlimited reactions would drastically increase the total damage potential of everyone and everything when the game already favors total damage potential over healing/damage mitigation options.
So yeah I'd say no thanks to unlimited reactions myself.