I've been thinking, and the way I see it is that the only way to make progressive elimination qualifying work would be to have a qualifying race (bear with me).
The cars could start the qualifying race either in a random order (determined by a lottery), or if excitement was what was wanted, in reverse championship order.
In order to lose the potential chaos of a standing start the cars have a rolling start, with DRS enabled from lap one.
At the end of the second lap the last car is eliminated. (So the car in 22nd places will start the race in 22nd place).
Then, at the end of each lap, the last placed car is eliminated.
This would mean that the director could always focus on the elimination battle.
It would also bring in questions about tyre strategies; if you stay on the same set of tyres, you run he risk of being an easy overtake. However, stopping for tyres will lead to the risk of being last!
By having the qualification race in reverse championship order forces the cars to overtake as well...