In civilized places, it was the other way around. Taxis exchange privileged position for certain requirements city demands them to meet as a part of city transportation infrastructure - requirements which include having proper insurance, servicing unprofitable routes, or adapting their vehicles for passengers with disabilities. One of the ways Uber saved money was by completely ignoring these market segments.
But of course, the major way Uber "blew taxi companies out of the water" is through their ability to offer below-market-rate prices by losing money on each ride, thanks to unending supply of VC money.
Uber definitely increased the availability and coverage of end to end car hire in my region. As far as I’ve seen, the evidence suggests that Uber is more equitable for geographic and demographic access.
But of course, the major way Uber "blew taxi companies out of the water" is through their ability to offer below-market-rate prices by losing money on each ride, thanks to unending supply of VC money.