Uber likes to claim that it's just an intermediary between independent drivers and riders, like an ebay for transportation.
If they really believe this, then they should do what bona-fide intermediaries do, and let the drivers set their own prices.
Doing that would solve lots of their legal and PR problems, from running afoul of independent contractor laws to customer complaints about surge pricing.
So why don't they do it? I suspect it's because Uber knows that the price drivers are likely to charge is higher than the price riders are willing to pay, once Uber takes its percentage. The only way to get the two sides to meet is to either artificially limit the number of drivers (which is what municipal taxi medallions do), or become the only game in town so drivers have no choice but to take Uber's prices if they want to find riders.
It's possible that Uber can eventually solve this problem by building out its own fleet of self-driving cars, but that's still years away. In the meanwhile, the company is a house of cards, requiring enormous ongoing capital infusions to stay in business. They can keep it up as long as enough investors believe they have a shot at becoming profitable someday. But if there's ever a whiff of trouble in raising money, the whole thing is likely to come crashing down remarkably fast.