That sounds like a good idea. You're right, people who abandon games when they're losing are a real pain. Happens quite a lot, too.
Game abandoners?
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Pretty sure chess.com already has a similar policy in place. Been awhile since there was a thread on this but if memory serves me correctly you have no more than half the total time of the game to make each move. Unfortunately memory rarely serves me correctly these days so I could very well be wrong on the specifics. I do remember a hue and cry from certain quarters that chess.com was reinventing the rules however. Don't know if the exact policy ever made it into the FAQ's, but you could check the forum archives....
Sometime back I used to play on a site called alilg or something like that. They had a timed-variant: 5-minutes for game, 2-minutes for move. So if you didn't move in 2 minutes, you lost. There was also a 3-game-1-move variant. I know people have connection problems sometimes, but those of us willing to risk should be given this option. I'd rather lose a few games due to bad connection than have to endure a whole lot of folks who abandon losing games. They are such a pain and I'm seeing a whole lot now.