Most of these organisations were mutuals, eg, member owned, and would have pre-existing relationships with doctors etc that would control costs.

In this way, there were no perverse incentives - people had "insurance", and they wanted that money to cover as many eventualities as possible. The bigger the pot of money, the more resilient the community.

So actually, health insurance has a long legacy. The problem, I would suggest, is shareholders who are not the principal beneficiaries of the service.

FWIW, in the UK we found that a system of mutuals and municipally owned hospitals was sufficiently imperfect that we created the NHS anyway. Probably best to skip to single-payer in the US, imo.