So having watched this so-called "disaster" for Bahrain (and not thinking that it was terrible), I think I understand both what the intent of the plan was and why it doesn't work.
The intent of the plan is to draw out the tension of the session, where the number of eligible running cars is reduced as time goes on. The idea is that things get more and more frantic as the bar for continuing rises and rises.
There are two reasons why it doesn't work: the cars, and the sessions.
Firstly the cars. Modern F1 cars have evolved into these complicated science projects that are good for one thing -- running Grand Prix races. They are not suited to an elimination style qualification. The cars basically have one good timed lap in them, so we get the situation that we have had for the last two races: everyone boils out of the pits, sets one time, and that's it. There is practically no chance that a team could turn a car for a second timed run, and since for the first two sessions the number of cars being dropped is relatively small, for the vast majority of the runners there is absolutely zero point in even trying. Thus, empty track time. If you send a car with enough fuel for more than one timed run then you will be compromising both runs since you A) have to carry around the extra fuel for the extra timed run(s), and B) you have to go easier on your tires so that you don't root them out too early. Neither situation is conducive to setting a time which is ultimately competitive.
Secondly, the sessions. Since qualifying is still broken up into Q1, Q2, Q3, then for the majority of the field there simply is no incentive to even try to run a second time in the session -- the times are set, and moving from 10th to 8th means nothing in Q1.
So here's my idea for solving both problems:
A) Make the cars start on race-fuel (or some common, minimum fuel level; and B) run qualifying as a single session, with the elimination starting after 10 or 15 minutes.
Presto, everyone has to look after their tires; the cars get faster as the session winds down; everyone would have incentive to keep running to keep burning off the fuel load; changing to the softer tires would become a strategy as to when you'd do it; and setting times would always be relevant because the times are always live.
You'd also get an hour of on-track chaotic running which the media thinks the man-in-the-stands likes to watch.