Regarding your 1st point, yes, it is a problem that cars are underutilized. So I think that in addition to promoting public transport, for the time being, we could also promote proper usage of cars. Here in Europe, we don’t have much problems with cars compared to US, but oh boy you guys overseas need to tame your F-150 owners.

Regarding the 2nd point, it’s not a fact but an opinion. With which I don’t really agree. I believe that true self-driving cars will eventually surpass the capabilities of meatbags, but I will look up the literature. Solely based on what you said, it seems to me that the “dead heading” problem is just a logistical issue that can be solved using science/technology (if the fleet of cars is algorithmically dispersed enough, they will always pick up a nearby passenger, as a hypothetical solution).
But yes, the corporations remain an issue and they will surely find a way to mess everything up. That is a separate problem that also needs solving, capitalism and overconsumption.