I work in insurance, but not specifically in-depth on regulated insurance rates like personal auto.
That being said, I can add some insight. Most state insurance regulators require a company to justify the rate they're charging based on actual claims data (i.e. you wouldn't be allowed to use a competitor's pricing as a justification). Insurance companies would basically never share their claims data with their competitors, so there's functionally a ban on using competitor's data.
Any rate changes have to be justified (based on claims frequency and experience) to the state regulator. I don't think it's a perfect system by any means; insurance commissions aren't completely unbiased, and there's some flexibility in what data the insurer uses. But in my experience it's pretty effective at regulating the data you can and can't use.
The ultimate outcome is that most insurers in these markets run combined loss ratios of greater than 90% (so on an underwriting basis, more than 90% of the premium they earn goes to paying claims and overhead associated with managing those claims).
I think the model of "here's a regulatory body, justify what you're charging based on this set of allowed data" is a decent framework, even if it doesn't work in every market.
If you're curious, the SERFF website [0] has rate filings for a lot of states. So you can see when a rating factor changes and what it changed to. Most of the detailed claims data isn't available for data privacy reasons, but depending on the state you choose, there will be summary figures available.