1) Ubers can avoid poor neighborhoods at will, and there's really nothing the city can do about it. I live in LA, and if you live in, say, Watts, you must call a cab if you want a car, no Uber will find you there, because it's "the ghetto" and there's never an Uber within 20 minutes. Taxis can be and are required to pick up from all parts of the city, and their statistics are closely monitored by regulators to make sure they do.
Yellow cabs in NYC absolutely do this. Yes, they have to take you to your destination, but that's it. There's nothing requiring them to drive around looking for passengers- hence why the green outer borough cabs came to be. Even in parts of Manhattan, you'd have to wait 10-15 minutes, or more during off-peak, before seeing an available taxi. If you walk a few blocks, they're all over the place again. I used to frequently visit a friend in the Lower East Side public housing; for her cabs were so rare she would always call black car services, which cater to the area with cheaper prices than a regular taxi.