Uber and Lyft actually succeeded in creating an accessible system that everyone could afford. You have it all backwards. The common person can actually afford Uber, not cabs.
A button that calls you an Uber is as easy to build as a button that calls the taxi dispatcher for you, but I don’t think the elderly appreciate the taxi experience of demanding cash because they’re pretending the card reader broke.
(You can already get a voice assistant to book a ride for you too.)
Ask your grandma etc if they would use that. Anyone above 50 these days will probably not give you a nice answer to having to use smartphones or voice assistants that usually understand less than a newborn child.
As someone around that age get off your virtue signaling high horse. People in their fifties today helped build most of the tech you use every day, but even if they hadn’t your implicit ageism levied in service of an accessibility rant is a level of irony that just can’t be ignored.