They already have a rule sort of like this.

Basically if you receive any sort of treatment, you are forced to go off the field after receiving said treatment until the referee says you can rejoin.

Personally I hate the rule though, because you get players that are legitimately injured and need to get some treatment, and then by the law of the game they have to they go off the field even if they don't need to get any further treatment at the side of the pitch. It punishes the innocent as well as the guilty.

Your rule would make it even worse though. I mean say Messi got injured playing for Barcelona and was bleeding. This happens often in a game but they can quickly bandage it up or even stich it up very quickly if need be and then continue playing. It seems though you're implying that it should be a rule that this player should be forced to get subbed off instead? Doesn't sem fair at all to me.