How will it reduce demand for parking? Do you envision the car will drop someone off and then drive away until it finds a parking spot that's farther than the person would want to walk?

Plenty of high demand areas use human valet parkers for this issue. The driver drops off their car at the curbside destination, and then valets take the vehicle and park it in a designated area that saves the car driver some walking.

Then, the valet parking area in dense areas has tighter parking where cars are allowed to block in others. As a result, the same amount of paved parking spot can accommodate more cars. That's why in a lot of dense cities, garages with attendants you leave keys with are cheaper than self-park garages.

Automated parking can therefore achieve higher utilization of the actual paved parking areas, a little bit away from the actual high pedestrian areas, in the same way that human valet parking already does today in dense walkable neighborhoods.

and people wouldn't be happy waiting 5-10 minutes for their car to navigate back to them.

As with the comparison to valets, it's basically a solved problem where people already do put up with this by calling ahead and making sure the car is ready for them at the time they anticipate needing it.

Once again reinventing buses and trains

Yes! And trains are very efficient. Even when cargo is containerized, where a particular shipping container may go from truck to train to ship, each individual containerized unit will want to take advantage of the scale between major hubs while still having the flexibility to make it between a specific origin and destination between the spokes. The container essentially hitches a ride with a larger, more efficient high volume transport for part of its journey, and breaks off from the pack for the portions where shared routing no longer make sense.

The challenge is one approach only needs to modify the transit infrastructure. The other means having to tear down and build new commercial and residential properties and force people and businesses to relocate in order to have a vaguely sane transit system. My area desperately wanted to do transit but even with rather significant hypothetical funding, they could only service about 10-15% of typical trips. They've settled on a plan that is much less money, but only serves like 5% of trips. To go with that plan, they are making restrictions around zoning to force mid density mixed use construction only, favoring one of the two chosen transit corridors.

They are trying but just people are distributed very awkwardly for mass transit.

I'd actually be genuinely curious to see how it compares to taxi drivers, bus drivers, or ubers. Since they drive professionally, you'd hope they'd drive a bit safer than the average human.

I'm sure nothing will be able to compete with the safety numbers of trains or just being close enough to walk though.

While I'd absolutely love better and more public transit, it just doesn't make sense in a lot of areas that are too spread out or don't have enough people per square mile.

To be fair I don't have 100% confidence that self driving is safer than human driving. I just believe that based on the current data, it seems to be. If new data comes out tomorrow, then I'll look at and evaluate that data.

I also don't believe that investment is a zero sum game. We should absolutely be investing in both. Both are valuable. You don't have to only invest in one.

I believe china has self driving trains.