So I well agree that Uber's technology, for which there are already multiple equivalents, isn't important. The contest will be entirely about business models and execution. IMO, that can be a lot harder to predict, at least without considerably more depth than I currently have on the players in this market.
By and large, people seem to love Uber. If they fall out of favor, I think it would be more natural for competitors to put pressure on them to improve (or supplant them), not city governments.
They use the public transit available to them where they move to? Why would self-driving vehicles not be like the postal service, a business but also an essential service?
Just because I left Chicago doesn't mean I get to take the Metra and the CTA with me.
Uber is simply an app with supply/demand machine learning, an army of drivers who are becoming more irate by how they're being treated, and community managers. What would it cost to reproduce Uber's app and backend? $500K? $1 million?
What happens if cities simply say, "You're out Uber" and buy their own self-driving cars for their citizens? Is Uber going to build their own roads?