No. This is a horrible idea.
HOWEVER, what would be a good idea is something along these lines...
Let's say you get matched with Troll A. You lose, you report him, and you want to start another game. Well right now you have to wait like 5-10 minutes to make sure he got into another game if he queued up, but sometimes you STILL get them again.
I propose we get a button that prevents you from getting into another game with them, but to prevent it from being abused, it will be at your expense. For example, if it would match you in a game together (on the same team), it would just ......... not. Like as if you weren't queued up at all. It would let him get into a game first, and make your queue time longer since you cannot get into the game he just got into and are forced to wait until the next available match, but it would GUARANTEE you won't get him again (or at least on your team). And you'd actually get into game faster with this system than the way it is now because you wouldn't have to wait or guess when to queue, you could just let the system get you the fastest possible match WITHOUT them. More people would be willing to requeue right away because the chance of getting your LP back is significantly higher with this system than if you just queued up right away and left it up to the matchmaking which WILL put you back together (since you were close enough in MMR before, and both lost MMR)
Maybe you could only use one or two a day. I mean hell I'd be cool with it costing a few LP, I would have had to dodge anyway but at least I don't have to wait a long ass time and can get my LP back quicker. And it could assist in flagging peoples' accounts if people consistenly use this on them. I mean if no one wants to play with them.... well why should they be in the game lol. Could make investigations into them much better than the throwaway report system which rarely actually deals with the people who need to be perma'd.