My mom has had State Farm for decades and has always thought they treated her more than fairly when there have been claims (in the early 90s after a hurricane, and in recent years for her car). In fact, they ended up totalling a very new Lexus SUV due to rodent damage (the car had less than 150 miles on it) and a year or two before she’d had an accident that was her fault.
In terms of car insurance, I’ve been hit by a Progressive driver, and they took care of things well. When I hit a driver, my Geico insurance also took care of things well.
When I had AAA home insurance after a hurricane basically totalled my house (Hurricane Katrina), I had one of the best experiences out of anyone I knew. It wasn’t a fast process, but it was faster than most others.
We have ASI (which is related to Progressive), and at first they gave a low-ball estimate of some roof damage, but after more documentation was provided, they ended up covering the bulk of the roof replacement (again, after another hurricane). (We only had to pay for an upgrade for the roof to sustain winds of 150 or 170mph, whereas I think they only covered 130 or 150mph.)
And, unsurprisingly, our state has a hard time getting home insurance companies to come to our state. Companies like State Farm only cover you if you are an existing customer, but they haven’t written new policies in about 20 years. And yes, our home insurance rates are quite expensive (as are our auto insurance rates…I recall moving to Louisiana back from North Carolina, and my car insurance doubled due to just the change in location).