I still do not believe it is USASF's business whether you have health insurance. That doesn't mean I am anti-insurance. There are plenty of things that I personally believe all citizens and visitors SHOULD/SHOULDN'T do, but I don't think that USASF needs to check as athletes walk on the mat. (have current car inspection, returned all library books, gotten teeth cleaned, donated blood, paid rent, called your parents, voted in elections, etc.) The only things they should be worried about are whether the athletes are age-eligible and are members of the gym they are representing. They should also have the authority to regulate some specific behavior that directly impacts the safety of the participants at the event, such as underage alcohol consumption. (Even that should probably just be handled by the local police, IMO.)
Part of it is philosophical (libertarian), but a big part of it is practical as well. USASF has it's hands more than full trying to be an efficient governing body of a diverse sport. There is no need at this point to make things more complicated for them, which adding immigration or insurance checks to registration will do. They should be focusing on the core issues and doing them well, rather than adding layers of paperwork, IMO.