One must read the whole thing to understand it. If certain organizations can just choose to not do business with you and the de jure system says that the only way to get a legally required document is through those organizations, then those organizations are a proxy legal system.
This does not seem particularly controversial to me. Yes, credit agencies and banking approximate such a proxy in the US but the limits of such a system in the US were tested when marijuana and pornography sellers were able to find a way to bank despite the rest of the system attempting to stop them.
I can't legally drive without car insurance, and insurance companies can just decide not to do business with me.
I can't get the service of TSA Pre without going through a private corporation that can easily decline to do business with me.
Our national parks are largely run by (private) concessionaires. While I've never been banned from a national park, I bet I could be de facto banned from, say, Yosemite by pissing off Aeromark enough, even if I didn't violate any law or do anything against park rules.
Almost everything you said is wrong, except the requirement to get car insurance. There will always be a car insurance company willing to do business with you, they'll simply charge you higher rates if you have no other options. (It's called "high risk" auto insurance.)
TSA Pre-check is operated by the federal government, but I assume you mean the LiveScan portion of the application process? That service is offered by both private companies and public agencies liked the DMV. The rest of the application process can be handled by the applicant, though you're also free to pay a private company to manage your application.
The national parks are run by the NPS. The concessions are run by concessionaires. If you piss off Aramark, you might not be able to buy anything from their restaurants...until you switch credit cards. But they have no control over banning you from the park because the NPS rangers control park entry. Also, concessionaires only operate some of the campgrounds in national parks; in Yosemite Aramark only operates the "lodging" facilities (i.e., hotels and the fancier tented campgrounds).
Right, but the state does not mandate you receive insurance from a single company. You could, should you do desire, set up your own insurance company. There are open regulations that can be obeyed by anyone.
TSA Precheck is administered by the TSA AFAIK, which is a DHS agency, not a private corporation. It's been a while since I signed up but IIRC it's run by the government.
I actually believe that if Aramark (I assume that's who you meant by Aeromark) didn't let you visit Yosemite and you legally are allowed to, you'd probably win against them in court (in contrast to what's happening in Sweden).
TSA precheck is run by private corporations - the TSA are of course the people that operate the actual airport, but the corporations are the people you sign up with that assess you.
Aramark (you're right, my mistake) couldn't ban you from the park, but they could definitely ban you from their campgrounds. So you could drive into the park, but you wouldn't be able to camp in most of it (except for backcountry).
I'll grant you the competitive marketplace for insurance, though I'm not sure it fully eliminates that point.
This does not seem particularly controversial to me. Yes, credit agencies and banking approximate such a proxy in the US but the limits of such a system in the US were tested when marijuana and pornography sellers were able to find a way to bank despite the rest of the system attempting to stop them.