would a tournament that started with a random, reachable middle game position be a good idea? There could be a different position each round, games would progress much faster....

great idea...but there would be a lot of things that would have to be worked out..

such as?.....

how to come to a balnced position after the opening.
If the position would be too onesided you would get a lot of rounds without knockouts...
On the other hand the position should allow for some tactical manouvering (no overanalyzed positions that lead to draws...