> Once the monopoly is out, Uber will just be like every other taxi company. And better still, all the taxi companies will be like Uber.

That is pretty much how things are here in Lithuania. The system works well, you don't really come across drivers or cars with issues, and there isn't really any kind of monopoly. There aren't many true taxis, because being a 'taxi' vs a 'private driver' means you pay more effectively just to be able to drive in bus lanes.

Historically people would phone up to book (and a car would turn up in under 10 minutes), but now you can use a single app to book and pay by card with all the different taxi companies (and get whatever car is quickest or cheapest). Uber were late to the game when they entered the market in 2015, and their launch has gone pretty much unnoticed.