I don't really believe that this is needed, although it would take a big burden off of the host when time limits are strictly enforced.
Yeah, it's really a way for the host to not be turned into the bad guy.
But, the override should exist. If all the players say "override", due to extenuating circumstances or whatever, then it can be delayed.
You're right that it won't save much time. But, it WOULD cut down on the biggest time-uses, by definition. Granted, it only knocks off the end of that time span, but, still, it would be something. And, it doesn't change the underlying game to do it.
One thing I forgot: The time increment should be variable. I'm using 24 hours because that's the most common number, but any number might be picked.
At LAST! The greatest campaign board game of all time is finally available for the PC. Can my old heart stand the strain?