You know that taxi services are treated much like an extension of a city's public transit right?
Taxis were given artificial monopolies if, and only if, they agreed to operate under certain rules. For instance, taxis cannot refuse to pick you up just because you live in a poor neighborhood or because you live too far from city center.
The taxi business, for many cities but not all, acts as an extension to public transit, allowing elderly people on the outskirts of town, or people in poorer neighborhoods, some way to get to their doctors appointment, or some way to make it to a job interview.
Uber doesn't want to follow those rules. Their drivers want to hang around the most lucrative spots, usually downtown business areas, and can refuse to come pick someone up if it is too far away.
In a perfect world, cities would build out their public transit better, but cost/time/competing priorities have always been an issue.