Can you describe the steps that would lead to Uber becoming a monopoly? I can't imagine that happening without government help, can you? And if it requires that kind of help, is the problem with Uber or government?
Uber only becomes a monopoly if they can keep all competition out, not just taxi companies. Taxi companies succeeded in doing that for decades by colluding with politicians to limit competition. Uber would have to adopt a similar strategy to get anything close to a monopoly.
Driving as a service always operates on public infrastructure and medallion systems are there to protect those commons from excessive use. If uber does not like the rules of road use, they are free to purchase their own right of ways. It's America, nobody will stop them if they show up with enough cash. Also, no more speeding tickets for uber drivers!