I’m so glad I’m not the only one to have thought “isn’t this just a natural consequence of the (optional) hitting cover rules?”
I disagree. Unless you’re using the optional Facing rules (which I personally like, but I know I’m in the significant minority on), it shouldn’t matter which direction attackers target you from. It’s assumed you can freely change the direction you’re facing at any time.
Well, if you’re using the optional Facing rules, you can just change facing as a reaction; no need to use the Ready action to set it up. On the other hand, if you’re not using those rules, a reaction shouldn’t be needed to change what direction you’re facing; if you’re grappling someone, you should get half cover in all directions (which could cause attacks to hit the creature you’re grappling if you’re using the optional hitting cover rules.)
That all said, I do think using the Ready action to grapple someone in response to being targeted with an attack seems like a solid tactic, especially if the optional hitting cover rules are in play.
Tavern Brawler and the Unarmed Fighting Style certainly make this tactic even stronger. Again though, I don’t think a Ready action would be necessary to interpose a creature you already have grappled between yourself and an attacker. If you’re using the optional Facing rules you can do so as a reaction without having to Ready it, and if you aren’t it isn’t even necessary to use a reaction to do so.