I don’t call this “who deserves it” because I don’t think someone who leaves a game deserves some sort of punishment for doing it. Don’t call it a punishment, because it isn’t. If someone leaves a game, either connection issue, leaving for a good reason, or leaving for no reason whatsoever, it’s a loss of time for the players the DC left behind. We’re trying to make the queue better for them not worse for the dropped player.
If it’s connection, a 15 minute time-out may likely expire before connection issues are sorted, and if they aren’t, it’s a safeguard for the next group being guaranteed that this won’t happen to them.
If they have to leave, or just decided in the middle of the game that they are done for now, a 15 minute timeout isn’t going to affect that at all. If they really need to leave, they’ll probably leave for more than that, and if they’re burned out for the day, that’d be some excellent burn recovery to return before that.
The only situation where a 15 minute timeout (the OP’s original suggestion) is really a setback is if you join a game, don’t like the settings, quit because of the settings, and re-queue immediately. In that case, it’s a setback for the one player that wants to play the one true map and a boon for the rest of the queue who doesn’t have to worry about being paired against that player for 15 minutes.
Right now there’s no system to dissuade this action, and I don’t think it’s out of the question to suggest a very temporary queue restriction would help to deter the behavior, and even if it doesn’t, it’d reduce the frequency of the queue being subject to an Alt+F4