Governments have not seriously tried to stop Uber yet. If/when they do, they will easily succeed.
Right now, the farthest most have gone is fining drivers a relatively small amount, which Uber pays. What happens when they step that up to seizing the car? Who is going to sign up to be an Uber driver in a city where it can get your car seized?
Here's how I predict it will go down. Cities will eventually decide to legalize Uber-type services, with such companies required to obtain a license. There will be a limited number of companies licensed in each city--it makes much more sense for the city and its citizens to have a small number of healthy companies than to have a large number of companies barely scraping by. Those licenses will go to Lyft and other non-Uber services, because they have not had the "fuck you" attitude that Uber has.
That's when the cities will crack down severely on Uber.
They're doing well but I don't see anything that would stop government regulating them out of existence. They're no, say, Bitcoin in that regard for sure.
*gross revenue. Big difference.