I'll be the lone objector. And this is just advice from a former insurance adjuster from many years ago. I have no idea if this system still works this way or not. This advice has nothing to do with the insurance company you choose, but about changing policies.
When you file an insurance claim, especially if the accident is your fault, the insurance company always looks to see if you're worth the risk or of they want to pay the claim and then cancel your policy. Other options are raising your rates and letting you keep the policy. When making these decisions, one of the big factors they look at is how long you've been with the company. If you've had the same insurance for 20 years and never made a claim, and now you cause an accident and have a really expensive claim, the fact that you've been with them 20 years is going to factor into their decision about what to do with your future policies. If you've only been with them 3 months and all the sudden you file a really expensive claim, there's a really good chance they'll cancel your policy. And guess what happens when you get canceled? Good luck finding affordable insurance again.
I've had my car insurance with the same company for 35 years and my RV Insurance with the same company (Progressive) for 12 years over 2 different RV's. Before I'd personally change policies the savings would have to be hugely significant. And although I always see people talk about Progressive raising their premiums, they have never raised mine significantly. I just checked the last 5 years records that I have, and it looks like the policy has gone up by about $150 over that 5 years.