They're very popular in a lot of places that aren't the USA (and even exist in NYC):

Dolmuş in Turkey: https://en.wikipedia.org/wiki/Dolmu%C5%9F

NYC "Shadow Transit": http://projects.newyorker.com/story/nyc-dollar-vans/

More broadly, "Share Taxis": https://en.wikipedia.org/wiki/Share_taxi

The idea isn't anything new, but being able to pay and ride from the convenience of Uber is nice.

I think it becomes something different and much more efficient with enough data and good algorithms.

It's worth noting that the ones in NYC are illegal. With that said I'm all for moving mass transit in this direction.

They are illegal to street-hail— but this is unenforced. The city is working on normalizing them, including adding taxi-like branding: http://www.nyc.gov/html/tlc/html/industry/vans.shtml

Most private buses in the third world will do this.

For the passengers who are onboard, sure, but what about pickups?

Call their cell. It's written on the bus.

It's exactly how taxis work in St. Thomas.