I speak from the perspective of getting the insurance company to pay to repair your car the right way. Geico is the absolute worst at that. End of story there. I'd take a Fred Loya job any day over Geico. Progressive used to be second in line to them, but they are getting much better. With documentation and a little work on my end we can get Progressive to pay correctly.
The best ones out there are Farm Bureau, Ag Workers, and United Fire.
Allstate, Liberty Mutual, Safeco, Farmers, Progressive, USAA, and Nationwide and a few others are good to work with too.
I used to put State Farm in the list above with Allstate, but since Covid hit they have gone downhill. State Farm will end up paying most of the estimate although they are getting worse too. Getting them to do supplements takes way too long. We had a car in the shop a few months ago that took 3 weeks to get a supplement approved. Then when the customer's rent car coverage was up after 30 days, they wouldn't extend paying for the rent car even though they were the reason for the hold up. We've dealt with this kind of problem with State Farm every week for two years now.
Every insurance policy states they can (and will) use aftermarket or used parts to repair your car, even if your car is brand new. Many customers come to me assuming their insurance will pay for OEM parts. Some companies offer "OEM riders" making them write the estimate using OEM parts only. I have that on my own policy. Read your policy. I never used to, but with cars becoming more and more complicated and expensive to fix, insurance companies are finding more ways to save themselves money when it comes to paying out.
One other thing we have found out is that most agents know nothing about the claims process. They sell you a policy but have no clue what they are selling. They never tell you that their policy states you will get aftermarket or used parts, etc. Of course most people only shop on price so they don't have to know. What good is saving a few dollars on insurance premiums if the company won't pay when you need them?
Also, make sure you have rent car on your policy, unless you just have lots of extra cars you can use. It's too cheap not to add.