Out of all the suggestions posted, I find that the idea of someone being 'unable to join another match until the one they left ended', sounds best.
For people leaving for an emergency, they obviously won't be back. People who leave because of griefing have to deal with a minor inconvenience. The only players really affected would be people who rage quit constantly since most of their time in GoIO will be on the main menu.
If I were to quit for whatever reason, I'd have no problem waiting for 10-15 minutes. I could go get something to drink, munchies, smoke break, restroom break, etc.