There's a few obvious exceptions, but plenty of insurance isn't required.
You're required to get homeowner's insurance if you have a mortgage, and you're required to have car insurance if you want to drive a car on public roads.
So the majority of Americans are forced to purchase at least one of these in order to live their normal lives, which makes demand inelastic.
It’s mostly your own governments fault if you can’t find a cheap policy, there are millions of people who will probably never have to file an insurance claim in their life making up for government decisions to insure people who wouldn’t normally be able to be insured because of poor decision making skills.
But that doesn't imply what you're saying unless the supplier has monopoly power, which they, by law, do not.