This pretty of close, but a little off. You are correct that they are heavily regulated because auto insurance is mandated by law, but mainly pertains to what they are allowed to charge for. In the US, each state has a DOI that checks over models that car insurance companies use to charge people. There are a lot of rules about what can and can not be rated on. T̶h̶e̶r̶e̶ i̶s̶n̶t̶ r̶e̶a̶l̶l̶y̶ a̶ l̶e̶v̶e̶r̶ f̶o̶r̶ 'I̶ w̶a̶n̶t̶ t̶h̶i̶s̶ m̶u̶c̶h̶ p̶r̶o̶f̶i̶t̶' o̶t̶h̶e̶r̶ t̶h̶a̶n̶ t̶h̶e̶ b̶a̶s̶e̶ r̶a̶t̶e̶ t̶h̶e̶y̶ c̶h̶a̶r̶g̶e̶.
Edit: (The comment below me is correct. I was getting a little hand-wavy. In general every part of a insurance plan will be scrutinized and has to be well supported. Insurance companies need to justify why there is a surcharge for some characteristic of a policy, this is what stops companies from just raking in money) They have to make an argument to the DOIs for why their base rate is what it is, so they cant really increase it for no reason.
The other comment in response about loss ratio is correct