CityMapper, a local transport app, tried to do this in London a few years ago.
It was a failure because they couldn't compete in price with the government-subsidised buses, so the vans they used were almost always completely empty. It was also a bad service: the few times I took it it was extremely late compared to the app time estimation.
I can see Uber succeeding if they have routes that are not covered by existing public transit, and are actually good at estimating pick-up and drop-off time to make a reliable service. This is a much harder problem that it looks.
It was a failure because they couldn't compete in price with the government-subsidised buses, so the vans they used were almost always completely empty. It was also a bad service: the few times I took it it was extremely late compared to the app time estimation.
I can see Uber succeeding if they have routes that are not covered by existing public transit, and are actually good at estimating pick-up and drop-off time to make a reliable service. This is a much harder problem that it looks.