If we’re going to opt for public ownership then why would you choose the less efficient single passenger method over already-established public infrastructure like trains and trams and buses which have been proven to work well in other countries?

Simple we have already chosen cars in the US. It is far easier to use the existing roads to our advantage then try and redesign the entire country to fit a train and tram and bus model.

Also please elaborate on how self driving cars will improve parking issues.

In a public car the car will drop people off and drive away to pick up other people. There would be no need parking at all. Just a small drop off and pickup location.

Now this won't work as well if we are talking about private ownership cars, but it would be better as the car can drop you off and then drive to a centralized parking location. This would remove the need for street parking or parking lots next to restaurants and stores. Or if your planning to stay a long time for exmaple if your going to work for 8 hours. I think many people might want rent out their car during the day. Car drops me off at work and I tell the car to join the "public car" network for 8 hours and it can go find some people to transport.

And as for traffic, while self-driving cars will be less likely to cause accidents and jams, hundreds of independent low-capacity vehicles are in no way more effective than a single locomotive carrying those hundreds of people in a smaller space.

Oh sure it won't be as effective but it will be much better then what we have now. And there are benefits cars have over trains. For example after a the world pandemic scare I find traveling in my own space a much more pleasant experience then sharing with many other people. Also I really like listening to music in a car as full volume very enjoyable experience that you just can't do on a public train :). A car will be a single vehicle to my destination, I can get in a fall asleep if I want. Buses and trains are usually multiple vehicles and you need to be some what alert to know when your stop is.