It wouldn't be an end to flexible work times, but due to per-employee overhead costs, the cost/benefit to the employer from the number of hours an employee works clearly spikes at a few different points due to overheads. At 0hrs/week, there is no overhead. At 20hrs, this is another ideal point since while you do have to give your labor a lot of rights, you don't need to offer certain benefits (vacation, sick pay, disability, health insurance) in many states (notably this works differently in california). At 40hrs, this is another good point since you don't have to pay overtime rates (but at least this cost isn't a big spike).

Basically there's a bunch of laws that spike certain expensive costs for employees if they work different amounts. Therefore its not very profitable to allow completely flexible work times. Otherwise many of their Hawaii drivers would drive for 21 hours for benefits, and the labor costs would be higher than if you were required to either drive for 20 hours or 40 hours.

I think ideally employees wouldn't be mandated to provide any expensive benefits to full-time employees and benefits would be centralized and funded through more taxation instead.

But mostly, uber is complaining because labor laws are complex

Not to nitpick in your post, but for CA this would be at 30 hours for the benefit of healthcare. CA Industrial Relations still classifies 40 as full-time, so unclear on what benefits are tied to that

Mandated wage guarantees and the costs of benefits would force Uber/Lyft to implement supply controls, which would result it a large fraction of drivers not being allowed to go online and drive.