It shouldn't be easy to stop enemies from attacking weaker characters. Some people complain the game is too easy and I think a big part of that is that they just have the monsters act like zombies. All characters should need to worry about defence.
Protection is better than people think it is. All fighting styles only activate x times per turn. None are 'always on' in the way you are using it. You wanted a way to protect weak party members, well protection is a good one.
Ranged characters and spellcasters should have limitations and weaknesses.
And also yes extra reactions would break the game. And also make it take far longer.
I agree that there should be some drawbacks to ranged combat (and casting spells). 5E has a few, but overall is not built that way. (Ranged combat strong options which have few -if any- downsides.)
The things I've mentioned go both ways. It is also difficult for the enemy to protect their vulnerable party members.
The issue with Protection Style is that there's a choice between being able to use the reaction to do something else (such as hit the enemy with an opportunity attack) and protecting. In contrast, Tunnel Fighter (Unearthed Arcana) grants an unlimited number of opportunity attacks (which I believe goes too far in the other direction). I wouldn't say that I feel Protection Style is bad, but there are times when it seems more difficult to use because it burns your ability to do other things.
While typing this, I had the thought that perhaps a fight with protection style should be able to use an action on their turn to give an adjacent ally the benefits of the dodge action until the beginning of the fighter's next turn (as long as the ally is adjacent to them).
Really though, the protecting people thing is only a small piece of what I'm looking at. Overall, what I'm looking at is making combat seem more fluid (and less stop-and-go) between turns. I'm aware (as others have said) that turns are an abstraction necessary for rpgs to function as a game; at the same time, some of the other games I play (and other editions of D&D I've played) had options for people to do things through a conflict.
Still, maybe it would break the game. I appreciate the input. I'm not concerned with things taking "far longer" because I do not believe that would be the case with the group I game with. (In my view, combat taking a while is more due to how 5E monsters use HP as a primary method of scaling.) However, I do think that this change may break parts of the game. I will consider it more.