Maybe we could do a nostr based application for founding and managing mutual insurance pools. You could join a grassroots pool of your extended family, local plebs or other group that trusts each other. Small pools could then unite as larger mutual pools that provide reinsurance.
This doesn't prevent officially incorporated pools from participating, but contractual, trust-based pools that keep their funds in bitcoin multisig could be operated without relying on government institutions.
One interesting idea is that you could appeal to reinsurers if your claim gets rejected on a lower level.