The many of the so called MMOFPS games are actually just a bunch of lobby and session games, with no persistent world.
Firefall is both a shooter and has a persistent world but it is also considered sci-fi.
Personally, I think the reason why it is so hard to translate something like Call of Duty or Battlefield into an MMO is that the setting and backstory doesn't really permit that element of anarchy.
That is to say that there are cops and they do a pretty fine job of keeping the streets safe from people armed with military grade weapons, people like your character for example.
Sure you could be a criminal and embody the anarchy. But you are not playing as a criminal, you playing as a soldier of the armed forces of so and so country. So unless you want to be causing diplomatic crisis's, you are only going to the places that you are to be deployed.
Of course, one can do what Ev E
does and isolate that pesky law and order to just one region of the game world. But then that implies civilization has already gone to shit, and all those spunkgargleweewees take place in a world that is about to go to shit.