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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

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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.
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It works even better with high demand because it's easier to find multiple people traveling to/from the same places.
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In principle, but there are hard physical challenges such as the lack of space efficiency between a typical four occupant sized vehicle and a bus that holds some 10 or 20 fold more people on maybe only double the road footprint. Time to seek out your paired ridemates is something to consider, it melts away as you pack more people into the same vehicle and increases both in time as well as space as you start introducing more lower capacity vehicles.
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You're not comparing against real-world fixed-route bus routes.

In the real world, most bus routes run nearly empty if not completely empty most of the time, belching diesel smoke and paying a driver, in order to ensure that service is provided to remote locations and that service is made available on a regular schedule. In cities, utilization is usually higher, although you see the same pattern off-peak.

In suburban and rural environments, the footprint is nearly irrelevant, but the lack of riders means that early attempts would start with designs that prioritize battery capacity and range over the sheer number of seats. In urban environments, the final mix of buses will look closer to a combination of mid-size buses for door-to-door and full-size buses for trips that are door-to-door but in practice are no different from fixed-routes due to the sheer number of people who take the current routes at rush hour.

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> 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.

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