That's not idealized capitalism, but utopian politics. You can only run that for as long as you don't attempt to describe the mechanics of the political system involved - at which point you will discover that even establishing ownership, let alone protecting it, and even establishing contracts, let alone arbitrating (not arbitraging) them, brings in the entire world of ideologies and wars and violence and so forth.
To criticize particular models of a society as utopian is, of course, valuable. I do that too. And, in particular, reject minarchistic models as utopian. Once a state exists, it will be misused, and no constitution will prevent this.
But your argument clearly overestimates the problems. There is no problem establishing contracts in a society with freedom of contract - this is a problem which can be solved by the people who want to cooperate with each other. There is a problem with finding an arbiter once some conflict occurs. This is the result of a failure of above sides, because this problem could have been solved at the time of signing the contract without any problem. Arbitrating is not for free, but this is part of the conditions of the arbiter. So, all this are solvable problems, and the solution does not even need a state.
Establishing and protecting ownership is a much more complex problem.
And if you want free market capitalism on top of it all, you're going to need a fully modern State of some kind - in particular, some kind of redistributive or "progressive" taxation setup. That's not an easy thing to set up and maintain.
First, the free market is not on top of it all, but the base. And, no, it does in no way need any redistribution, or even a progressive taxation. (Which is anyway only a propaganda lie, given that the rich will create and protect loopholes for avoiding this "progressive" taxation.)
it's flatly false in your first direction of implication (more reg, power, own -> more socialism: is false), and only partly true in the second (more socialism -> more State reg, power, own,: depends on what is meant by "more" socialism - if the ownership is community scale and below,
Fine. Given your style of discussion, one can never hope for more than a partial agreement in a partial direction, so that this counts always as much as complete agreement ;-) In fact, all what really matters is a correlation. I do not see here any -> of <-, they would make not much sense, because what would be the causality here? The only causal thing would be what happen if some socialists take the power in the state. Would this lead to more or less regulation/state ownership/state power? The answer is, I think, clear. And your point about communal ownership would be quite irrelevant for this.
And, I hope, you recognize that the difference between communal and state ownership may be formally very big, but is not essential at all from a libertarian point of view. The commune is usually nothing but the local representation of the state. The time when there was a really big difference, with towns being often independent political entities, are in the past, and the examples where they have yet some real power are not very much (Swiss, of course. Maybe in the US, I'm not sure.) Usually they are only administrative departments of the state.
one could in theory set up a socialist economy in which significant property was "owned" by a designated person - their responsibility to maintain, their injury if lost or stolen, their task to make productive, their privilege to enjoy and benefit by, etc. The designation would be made by some community means - no buying or selling involved. Does that clarify things for you? Note that this setup, or close to it, was once common in North America.
In some sense, this is simply the fate of any form of common ownership. Because a common decision making process simply does not work. So, common ownership usually ends with some particular person making the decisions, and de facto "owning" it, but only in some restricted sense.
To organize the things in such a way that the private interest of this de facto owner is essentially the same as the common interest of the collective which, in the propaganda, "owns" it, is the way to minimize the economic harm caused by socialism.
That depends on the setup. In the examples of communism that populated North America until recently, political power hardly existed. Even war was voluntary.
That means, these societies were, in these particular aspects, libertarian. Note that libertarians have no problem at all with volitional communities which decide to organize their community following communist principles. As long as these anarcho-communists accept that other communities may decide to organize themself in a capitalist way, no problem. The problems start with how the different communities interact with each other. Here, of course, one community has to accept the property of other communities, or the whole thing ends in a war between the communities.
Some cheap nonsense deleted.
For example: You don't actually mean anything in your posts here - anything at all - by the terms "socialism" and "capitalism", except the value judgments "bad" and "good".
Wrong. I have characterized, in some detail, the properties of ideal models of capitalism and communism. And without any value judgement applied:
In the idealized capitalist society, there is no such danger. The state is (idealized as) a state of law, if you do not violate the law, fine, your ownership is safe. In the ideal, political power gives you nothing - it is only a boring job to protect the ownership of others and to arbitrage contract violations.
The other ideal is the communist one. In this ideal, there is no ownership at all. So the political power is everything, and to add "rich" to "powerful" is only (considered as) a defamation of the powerful.
To illustrate: You are on record as claiming effective equivalence between socialism and corporatism - both "bad" - and capitalism and free markets - both "good". The only way to do that is to discard the meanings of those terms.
Wrong too. What I claim to be effectively equivalent is corporatism and the modern, social-democratic socialism, which no longer aims for state ownership of all means of production. Above being different from the well-defined ideal communism as well as from the well-defined ideal free-market capitalism.
Of course, I personally favor a free society. Because I like freedom for myself, and as well because I think freedom gives advantages to everybody. But does this mean that I have to apply cheap moral levels "good" and "bad" to them? No. I know that freedom, in a reasonable society, means also responsibility for the harm caused by the own free decisions. There are a lot of people who want to get rid of this responsibility. But without this responsibility, freedom becomes harmful for the society as a whole. This is the privatization of the gains, and socialization of the losses.