The idea is to make it a 1-sided marketplace. Uber's entire business model is focused around squeezing vendors - now they think they can squeeze Google if Google becomes their vendor instead of a bunch of independent contractors who are legally inhibited from collective bargaining? Uber has no idea how to be successful when the seller side of their marketplace is organized and plays hardball at the negotiating table.
Tesla and Waymo are arguably pretty close in self-driving technology, so there's already another player. Uber could just buy a bunch of Tesla's once their tech is good enough for autonomous driving.
The car companies will do everything to prevent Google from having that monopoly. E.g. Google could be forced to license their software. Then, Uber gets their 2-sided marketplace back.