Commercial air travel is one of if not the most heavily regulated industry in existence. As such it is subject to significant regulatory capture and cannot be considered a "free market". This is something a lot of "liberaltarians" or "lolbertarians" (not accusing you or the GP of this, but I have had to make this point to some people IRL) forget.

That said, even in AnCapistan airlines would have insurers who would probably have all number of policy riders that set standards for passengers who were an increased safety risk and whose passage on an insured aircraft would invalidate the policy. "Rule by Actuary" is a problem I've yet to see an AnCap give serious treatment to.