They might or might not. It depends on how trivial the ass-kicking is. A heated exchange and a couple of blows--maybe not. A hospital bed--count on action. The BIG thing that will change in a free society, which no one seems to take into account, is NO PUBLIC PROPERTY. That means the owner of the property will tell you what you best not be doing, and if you can't work out terms with him, you're not going to get access to his road, park, or whatever. If what you're doing is trivial, like showing boobs, he may decide you're not worth dealing with. If you're beating up his customers, it'll be an issue.
Think of it like what goes on in bars now, but without the big brother agencies who tell them how to run them. They'll tolerate some scandal, but not violence.
By the way, there never will be an anarchtopia. The term is offensive to intelligence.