... which would stop working if the computer went down.

You could even install rails that go along regular routes, and put on scheduled carridges that people could all jump into at designated places along the route.

The computer could generate a schedule and post it publicly so people knew when they could hop on.

You really don't see a difference between a public rideshare and public mass transit?

Finally a use case for the blockchain ;-)

Technically it exists, I wonder if that’s what they used. It’s called BlaBlaCar