> So it overall reduce the burden on the court system and the insurance self-finance itself, there's no need for profits.

Profit is seldom a significant part of costs. Slate Star Codex went into that quite a bit in the context of healthcare.

Cost explosions usually come when controls on costs are missing.

Competition can be one way to control costs, but it's not the only one. Eg tap water in most places or the Quebec insurance you mention are low cost, too.