Small self-driving busses would do exactly what you want. The cost of increasing bus service is overwhelmingly the cost of bus drivers. If the busses could drive themselves, cities could afford to deploy a lot more busses, especially smaller busses, running much more often.
As for light rail, in the US, light rail projects can typically cost hundreds of millions of dollars per mile. The NYC 2nd Avenue subway expansion cost billions of dollars per mile.
And, if you want people to stop wasting city space on parking, self-driving taxis are exactly the right solution.
If buses are autonomous, it no longer makes sense to have arbitrary routes that people need to wait at a bus stop for. They can wait in parking lots, charging their batteries, until they are summoned, and give people door-to-door transportation.
It sounds like an autonomous taxi, but not necessarily. A taxi usually has only one rider, whereas a bus would have more seats, and potentially pick up and drop off other riders that are more-or-less on the way. This is Via's Microtransit[1] model, but without the cost of a human driver, it becomes much more cost-effective to deploy at large scale.
[1]: https://ridewithvia.com/solutions/microtransit
That model doesn't really work with high demand I wouldn't think. The thing with the fixed route case is you no longer have to serve the many edge cases, you force people to solve it themselves and maximize the service you can offer over a more collectively beneficial routing.
> And, if you want people to stop wasting city space on parking, self-driving taxis are exactly the right solution.
Self driving taxis have to be parked (or cruise around continuously), I guess, and that parking better be close cause ain't no one waiting for a self driving car parked 30 minutes away to get moving.