I can't imagine not wanting insurance, much less resenting a "requirement" to do so. In my state, at least last I checked, drivers are not strictly required to have any kind of auto insurance. However, if you elect not to, you must file an affidavit of personal responsibility with the DOT/DOR.
Insurance, at least in the automotive insurance world, can cover so much more beyond the mere medical and property damage related expenses, including other lawyers paid by the insurance company to litigate their liability, not yours. They don't represent you of course, but your interests are closely aligned in many cases. Not always, but often.
I'm not rich. I have nice enough E36 M3 to care. I'm covering it with insurance.
The tort/legal system and the insurance system are not a new invention, and the associated theories of liability are not recent or american inventions either. It goes back a long way, to at least address the original question, being how did we get here? Insurance, much like the ability to incorporate, has done incredible things to advance society. We didn't just get here, it goes way back to before the East India Company.
The shifting of burdens and the taking of chances...
Now, we can talk about the refusal of insurance companies to pay claims in bad faith, and I will join anyone in being totally pissed off.