Although the thing that annoys me most about tournament play is people constantly complaining about having to wait for other people to finish their games, I would agree with this suggestion in principle. However, this would be on the assumption that although the tournament has progressed to the next round, the other games do continue, in order to fully complete each round.
Thus, those who want to complain again and again about having to wait to progress will be able to play their next round of opponents, and those who are just enjoying their games, despite finding themselves in a position which cannot see them progress, can still play out the remainder of their match(es) to their satisfaction and to perhaps gain the joy of finishing well in their respective group.
Hope that makes sense, I think I started waffling a bit towards the end!
I think once it is determined who will move on in a round, the tournament should go forward even if not all the games are finished.
This would speed up tournaments a bit and doesn't seem like a difficult thing to program. This is also one of the often complained about problems in the forums, tournaments slowed down for one reason or another (vacation or people who won't resign).