No one would work when you wanted them to work unless you make them. Would you work a busy Friday night dealing with drunk people and missing your friends when you could get the same money for doing nothing on a Tuesday morning?
I mean, what you're describing without realizing it is just a cab company except you pay everyone a 30+ hours a week for doing nothing on top of what you pay them for actually working...
This is why cab companies don't already let drivers pick their own hours (assuming they don't use the uber-lite approach of people just hiring the cab\medallion).
I get that some flexibility is lost. But I would argue that
1. It is by far not as bad as Lyft and Uber present this and
2. I think this is a good thing overall. Less payment flexibility means a more stable income. Sure, some drivers don't need that stability, but those who do need it, really need it and this is more important in my mind.
The second point also fits into the narrative that this only benefits 1/5 of the drivers but that these drivers are doing a majority of the rides. I don't have a citation for that, so take it with a grain of salt :)