If the issue we're facing is that refs don't want to card for "professional fouls" that kill the game and that refs don't want to send a player off for a second infraction, I don't see a "sin bin" doing much to resolve this. If a foul occurs after the 80th minute of the game, there would be no difference between a second yellow or a sin box. The team would effectively lose that player for the remainder of the game.
If refs are afraid to give that second yellow, why wouldn't they be afraid of using the sin bin...?