Uber and other ride sharing services are so much better than taxis, why would you want them to die? Uber's international support is amazing and has made international travel far more safe and convenient.
What Uber and others do is an unlicensed/subcontracted taxi service.
Private car hire where you book someone to drive from x to y location at z time has been a thing for a lot longer than these apps. That's what Uber and others do.
Taxi's can pick up people who hail them at the curb. That's their differentiator from private cars and uber. That's what they have paid licencing fees and bought medallions (depending on area) to be able to do.