Again, you are not permitted to STIPULATE that which you are required to DEMONSTRATE. Really, pointing out the same fundamental error over and over again is like responding to an ELIZA automaton.
On the other hand, imagine that we have anarchy and the present political system collapses.
Then, if somebody attempts to infringe my rights, I will have the minor inconvenience of shooting them and cleaning up the trash. A PITA, but that's life.
That the public square is domain of government is a valid assumption. Historically it has been; it was when the Encyclical was given; it is now. That in anarchy it won’t be is a hypothetical; if you want to discuss it further, perhaps this thread is not the best vehicle but briefly, I am game. Beyond “I’ll shoot you”, what makes you think that incidents of private suppression of undesirable speech, for example, at FR, are NOT going to translate to similar phenomena under anarchy?