More to the point, is there any legitimate basis for stopping Uber? I would say not.
Private cars spend 98% of their time sitting on the road doing nothing. It a horrific waste of capital, not to mention a waste of public real estate. Anything that mobilizes that capital is a good thing, especially if it gives people an incentive not to buy a vehicle of their own.
OTOH taxis will always have a place, especially if the taxi drivers can up their game. If they can genuinely offer a higher level of service, consistently, then people will still want to use them; Uber by definition is a bit hit-and-miss. Uber is not a kind of taxi service, even if it superficially looks like one.