This approach would require full transparency to be successful. That’s a stretch for Uber, but for all markets as well, because capitalism has tended to build profit based on information asymmetries. The “ability to trade with everyone” demands that Uber become an information conduit along the lines of a utility or a regulated trading system. That doesn’t seem likely.
Uber has tried hard to destroy itself. Its failure to do so — despite every infraction short of assaulting the customers — shows the powerful forces turning the ride-hailing app into a monopoly. Such dominance is good for neither drivers nor passengers. There is, however, an elegant answer: to copy the very symbol of free market capitalism and treat Uber like what it truly is, a stock exchange.