That way drivers could be more legally considered contractors (they set their own rates), and none would feel underpaid (after all they get paid the rates they set).
The theoretical ideal price for a ridesharing trip changes in realtime and depends on many different factors like how many drivers are nearby, how many other riders are nearby, each driver's willingness to drive to your destination, etc. Letting riders and drivers set their own prices would make the market significantly less efficient, and would make both the experience for both sides of the marketplace quite miserable, especially during events like demand spikes. There is literally a several hundred-strong organization at Uber (Marketplace) whose single focus is to make a maximally efficient marketplace. It's honestly kind of dismissive to suggest something like this, and to call it "a simple change".
Disclaimer: the above is not meant to be a representation of how Uber pricing works, just my own theoretical musing
(At least, that's my experience. I wonder what your data has to say on it.)
As a customer, I'd be happiest if taxi companies charged a rate per-km, that's calculated off their consumables + car amortization + some reasonable profit margin. I think drivers may be happier too - recent personal experience with myTaxi shows this. They offered a promotion in which the passenger would pay a fixed cost known immediately in the app, but which calculations changed every day or so. Some days, it would become a good deal for the drivers; other days, the drivers would be working at a loss. I had a lot of problems getting a ride when using this promotion, and chatting with the drivers revealed that they instinctively ignore those requests, as from their POV the profits are unreliable.
Sidecar was acquired by GM after it shut down at the end of 2015.
"given that drivers cannot set prices or market their personal services to potential customers. The driver’s entrepreneurial opportunities are almost “completely circumscribed by the company’s control of the price,” she said."
Yellow cab drivers agitated for banning Uber and instead the city government made them a ride hailing app where they can choose how much to discount over full price.
I haven’t used it, but know people who do. It’s kind of up to consumers to figure out how much to pay vs how much to wait.