Yeah, it's been a while and I don't remember any details, but my impression was no fault meant my insurance covered me and your insurance covered you, regardless of who caused the accident. That was my impression at least, and I don't remember anything being said about requirement (in other words, you may still have been required to carry insurance). But I could be wrong about all of that, it's something I vaguely remember hearing about, and it's possible someone tried it but it was way in the past. Or it's possible I completely misunderstood what they were talking about.There is no state in the United States that does not require "something". Every state requires either liability insurance, a fee paid to the state that is intentionally generally higher than the minimum coverage would be, a cash bond or deposit equal to the minimum generally required, or the ability to demonstrate the financial capability to pay for damage caused by them in the event of an accident. That is going to require most people to buy liability insurance to cover damages caused to others by them. That's a good thing. It just needs to be enforced more stringently. We are a nation of laws. Laws exist to prevent anichary and ensure our rights as citizens against abuses by others, including the government.
If there was in fact a "no fault" or more aptly called a "no responsibility" system, there would be nothing to prevent the streets and highways from becoming a demolition derby every time someone got cut off in traffic and had a little road rage. I don't think most people want to live & drive in a Mad Max type world, but then again, maybe some do.
Edit: Okay, probably should have done this in the first place but finally googled it, and seems to have more to do with medical claims than with damage claims.
https://www.carinsurance.com/no-fault-states.aspx