Why do we fear Laissez-faire?
Without the possibility to prove it, it is arbitrary and therefor a procedural proposal and procedure has little, if anything, to do with justice, which is why Nozick is not taken seriously by philosophers in Europe. Kind of like a footnote to Rawls if he's discussed at all. It's purely cultural that Nozick is considered an important thinker in the US due to its outsized individualism and Nozick is just an excuse to shore up anti-social laws.
Come to think of it, I fully support everything you propose to be implemented as quickly as possible in the US and watch it crash and burn as a result.
The fact you cannot prove that all transactions throughout history are just does not entail you cannot prove that some transactions are just. Some can be proved, some cannot. Therefor it’s not arbitrary and not procedural. But I'm disappointed that all we are doing is quibbling about the word "historical". It's so trivial as to be irrelevant.
It's a simple matter; if someone stole a bike and you receive it as a gift, that's not a just exchange. You are not entitled to it and ought to return it to the person it was stolen from. If the bike wasn't stolen and the exchange was voluntary, that's a just exchange. So why is state distribution of wealth just or unjust?
Europe has given us the collectivist and social politics of Communism, Socialism, and Fascism, which have spread worldwide, ruining every country infected by their ideas.