In the US, I think it's fair to say that the typical insurance policy is required somehow or another.

I guess there are lots of people that rationally purchase homeowners insurance, but there's also lots of people that purchase it as a requirement of their mortgage. Auto and medical both have lots of government rules that push people to purchase them.

Yes, but the compulsory liability insurance in my state is something ridiculously low (like $20K, IIRC). I carry a significant multiple of that, which is an example of buying optional insurance.

Life insurance is another purchase that's typically voluntary.

Different kinds of risk. Normal insurance doesn't care if the stock market drops 30%. Something guaranteeing payout for decades has to buffer against that possibility.