Insurance companies absolutely need profit. The basic argument is simple - insurer's capital moves like a random walk and if premiums equal claims (i.e., zero drift), that eventually falls below any starting level. In practice, that means that a failure gets socialized (e.g., state guaranty funds assess levies on the remaining, solvent insurance companies, which ultimately pass those costs down to consumers through higher premiums)

What we need is competitive markets, what we get is heavy intervention. For example, https://en.wikipedia.org/wiki/Certificate_of_need system means that to build a new hospital one needs to go to their direct competitors to ask for their permission. Imagine if to open a pastry shop you needed a permission from every other pastry shop in the city - bonkers.