If money is the dividing line between people getting shot and people not getting shot.... people will be shot.
And sobody who wants to have an abortion needs to go to arbitration first?
I guess you skipped the part where I said "and it risks lives"? Money isn't the only thing stopping a shooting fight over the issue.
And I take it you've never heard of "precedent". The first dispute - if that - would go to arbitration. All others after that would point to that decision and say "It's been done before. Now shoo."
Myrkul: it's wrong to eat your children, because you take away their chance of a long fulfilling happy life.
In other words, because it's murder. Unless you're suggesting that murder would be acceptable in an AnCap society (something even FirstIdiot hasn't had the audacity to try) then the conversation is over.
Now, because I promised:
Could you hire a defense company to intervene in a conflict you are not part of, to protect for example children, the uninsured, the mentally handicapped or demented elderly?
In a word, yes. It may end up in a rather hairy arbitration, but in general, you can defend a third party, and by extension, can delegate that ability.