This is something that has been bothering not only me, but plenty of other people, especially when trying to run an ARAM. Whenever we try running a match, it can take anywhere from 5 to 10 minutes just to get it started because of two types of people:
1. The standard "leaver"
Generally, this person joins the match, and once the match starts they find they have a champ assigned to them that they aren't particularly good with. If they can't get anyone to trade with them, they simply leave and re-join. Banning doesn't stop the problem as you generally get 3-4 before you finally fill a room with players who will stay.
2. The troll
This infuriates everyone all the more because they don't leave until the very last second. So all trades have been made, runes and masteries picked, and everyone has prepared to use the champ they have. All of the sudden, we're back at the lobby and have to wait for another player to join and then go through the trading process all over, and possibly go through a couple more leavers too.
A solution that I think would be very simple and efficient would be to add a box to have the Quit button on or off. I'm not saying this is a feature that NEEDS to be added, or should be added soon. I'm just asking that it be considered and hopefully added sometime in the future so that people who want to run games in custom, like ARAMs, don't have to deal with unsportsmanlike players and trolls.