There's no inherent reason it must be a profit-making business. Organizeing as a cooperative, mutual insurance is also an option. Granted that any version still must set rates that cover expected payouts.
Insurance is an extremely demanding business. This isn’t something you can throw commodity drones at. If you’re willing to create a coöperative job that pays millions to its actuaries and risk managers, fine. Most don’t. Hence why a profit-based model works: it can incentivise the people that are needed for it to work in the long run to do the job. (In the short run, anyone can run a sloppy insurance operation.)
https://en.wikipedia.org/wiki/Saskatchewan_Government_Insura...
I will never understand the endless linguistic indirection when in the end it’s all Soylent Green; just people.