Not sure if TERF Island with a Great Firewall is exactly better

Allowed? Technically yes, in the same way people are allowed to start local broadband co-ops or like grocery stores or whatever else.
The problem comes when you have to actually make people aware you exist and have a service or product for sale, and "compete" with the national/multi-national corporation who have infinitely more resources than you do.

Just look at how Walmart and now Amazon have put just about every mom and pop shop out of business. They can move in, drop prices so low locally long enough to put you out of business because they have other areas locked down already and covering the losses. Then once they have the market locked up they can charge whatever they want because you have no other options.

Almost certainly there already exists a non-profit health insurance organization, they just don't have the resources to advertise on all the major channels and across the interwebs like all the predatory ones do.