I took the phrase "legal backing" to be a euphemism for enforcement. i apologize if i misunderstood. Specifically what did you mean by this statement?
Let's just say some kind of legal framework in whatever form. There are several variations out there afaik, but I mean approaches in general that people like Hoppe, Tom Woods or Walter Block describe and that seem to be necessary to protect property. Libertarians take the concept of property granted somewhat as said, but this concept is debatable as there are other (more collectivist) points of view out there, but let's keep that discussion out of this thread.
And in that event, it is entirely within my rights to kick you out of my house, or take back my gold bar. I can exclude you from the use of my property, whereas I cannot exclude you from the use of the randomly generated private key.
Ok, the "but you can copy digital stuff" argument. However, let's assume private keys would never be "randomly generated", as laid out before (laws of the universe etc), but rather in almost all cases would be taken by force or by trespassing, where it plays no role whether it's digital or physical trespassing. If you sneak in and steal jewelry out of my drawer, I might or might not have a chance to catch you red-handed. Same with Bitcoin wallets really. I can also prevent you from spending my bitcoins if I catch you in time. How, you ask? Well I can tell you but that means I'd have to kill you. :·>
A bitcoin wallet can be protected with due diligence at limited cost, but catching a thief is expensive.
The cost argument is a good one and might be a good explanation of
why Bitcoin rather fits Stirner's philosophy. A question left to ask might be if it would always remain that way, or if there'll be scaling up libertarian cyber police brigades one day.
Protecting your house against outside attacks is different; someone with a tank platoon can take control of it on a whim because he happens to be passing by. If you use the Max Stirner stance from the OP on houses, what keeps your next warlord from just taking it?
That sounds a bit like the Mad Max argument against anarchism. I haven't looked deep enough into Stirner's philosophies yet to figure out what his stance on this would be. However, the power of the might and concentration of power in any form (be it sheer force, capital, or social engineering) is a threat to any society and might be the very reason why we still can't have anarchism in any shape or form.