Valid concern, tbh - but I guess (at least in London), you've got three/four tiers of cabs now - Black Cabs, Uber, Kabbee/TaxiCabit registered minicabs, and tiny local firms that aren't on those systems - I suspect it might be the last ones that either get squashed out or forced onto the new tech.
(Also - try getting a blac cab to take you back to Peckham from the centre of London basically any time after 6pm, nightmare. /sarfovdarivva)