I'm not any kind of anarchist or voluntarist, so I have a different perspective.
It seems to me that "private property" is an inaccurate description of whatever crypto-assets are supposed to be.
Suppose you own a forest surrounding a mountain, and I own the mountain itself. I could reasonably ask (or require) you to allow me an easement to that mountain, especially if there's no other way for me to get to my property. Perhaps, if I wished to start a loud, polluting mining operation, demanding a large road for trucks and heavy equipment to go through the forest, we would have to negotiate. But there is someone real--something you or I cannot dispute--on which the whole situation is based. There is a mountain, which I own. There is possibly ore in the mountain. You own the forest around it.
But suppose you own a forest around a large but entirely dead clearing. I say that, no, the clearing is not empty, there is a giant mountain in it (only visible to the worthy) that has many castles, dragons, waterfalls, etc. Since this is such an amazing mountain, I require you to verbally acknowledge its existence to maintain its property values, offer easements to those going to the mystical yet invisible waterfalls, and contribute to castle maintenance and the Space Witch Defense Fund--for Space Witches, you see, are the natural enemy of the dragon, and without dragons we would all be star-hexed.
In both of these scenarios there is someone that might be called private property. One of them, I hope, you will also find absurd.
Crypto is closer to the second scenario than the first--all our digital assets are merely numbers spread throughout the world. To say that such assets are "private property" and miners, or witnesses, or whatevers, must protect them by spending computational resources and other capital is like saying the treasures of the invisible mountain must be protected from the space witches, ergo someone must pay the dragon-riders. In fact, if code is speech, which sounds like a cool slogan, then any crypto-asset would result in compelled speech under this scheme.
The alternative--which I suspect you would agree with-is that, no, miners and witnesses and whatevers and all the other forms of dragon-rider are not compelled to do jack squat; they simply participate in this whole scheme voluntarily. Either for remuneration, or perhaps they really hate space witches. But if that's the case, then what exactly are blockchain assets? They do not merely only have value if other people say they do, but even exist in the first place only because other people say they do, and would all cease to exist the moment those other people quit.
Since when does the natural right to private property depend on other's running a certain version of software on their computer as opposed to another? I myself do not believe in an absolute right to private property--the Universal Destination of Goods is a superior principle, to which private property must bow in service. But that makes this situation all the more ridiculous, because if all the computational power in the world must be dragged off for some massive task, then of course we would have to stop mining and witnessing and whatevering to accommodate this greater need.
St. Thomas Aquinas speaks of the distinction between natural and artificial wealth. Natural wealth is anything that is of intrinsic use: horses, houses, and heads of cabbage. Artificial wealth is only that which has value sheerly because we say it has value. Cryptocurrencies, like all currencies, fall more into the category of artificial wealth. After all, you can't eat a bitcoin, fuel your car with ether, or paper the wall with steem.
Which comes back to the original point: crypto-assets have value in that people say they do. Are we required to say so? After all, Binance would be a far greater tyrant than any cabal of sybils, in allowing some assets to be valued higher and others lower, then allowing those numbers to change. If I dent your car and it costs you $300 to fix, then I am to blame. If I dump a whale-lot of crypto, and cause everyone's wallets to drop an average of $300, am I responsible in the slightest?
And yet--if I steal $300 from all y'all, I definitely am.
The only answer to this paradox, I believe, is that there some more subtle category than "private property" which applies to crypto-assets.
You touched on some things I've been thinking about before.
As to Universal Destination of Goods, that rubs me the wrong way a bit... it opens the door for religious or dogmatic statist control of everything "for the greater good" (for whoever gets to control that definition). Historically... I'm not a fan of that approach.