I disagree with some of your points, here's my take:

I came from a country which used to have publicly-owned assets, specifically gas and utilities (including communication/phones). They served a specific function, to subtly influence the market while still keeping it free. There were always private entities competing with it, and they still flourished by providing better service or value add, as opposed to the public option, which didn't advertise, and only offered the bare minimum (at a cheaper cost).

There was a major push to move to privatization after and it was great for about 2 years before it became a race to the bottom. Since the barrier to entry was so high, there wasn't really a free market for it, and things became an oligopoly and service went to shit. The old reliable ones are expensive and offered bad service, any newcomers get bought out or went bankrupt. I think public ownership is the middle ground, and needed to keep the "free market" truly free.

And not having anything other than equalizing resources is fine for now. As you said, it won't solve all problems, but it will solve some, and prevent others. Then, we can start looking at other problems and adjusting.

My experience working in different countries is that: a rich nation is not one where even poor people can afford cars. It's the one where even the rich people take the bus.