Go check out an independent insurance agent. It's not "gaming" it literally takes 20-30 minutes, and could save you $1500 over the whole year (especially if you have multiple cars).
To "nudge" you in the right direction, buy not switching, you're basically saying, "I make money at $1000/hour, so it's okay that I don't expend the mental budget to compare quotes".
You're right, though, that what insures promise to do and what they'll do are two different things - its hard to price that in upfront. I don't think the insurer in question, State Farm, is exceptional in that regard either. They dropped a family members coverage after 2 hail storms. They dropped a friend's company's policies after a single claim.
State Farm makes its money by bilking people with it's solo agent model. "Talk to your friendly neighborhood State Farm agent"...who only gets quotes from State Farm.
We would not do that in any other industry. Insurance is a commodity. It's like electronic items. We price hunt Amazon vs. Newegg vs Monoprice because we're nerds, we should do the same thing from our insurance providers.
You don't have to settle on some no-name insurance agency - you can set a high bar, but expanding your marketplace of options from 1 to 5 or 6 can only mean good things for you as a consumer.
Car insurance is definitely not like a given electronic item, which is made to the same standards by a single manufacturer. It it's like some nerd purchase, it's more like flash drives. In theory commodities, manufacturers have a complicated set of incentives and the actual quality of the product may be hard to determine without extensive use.
I'm not against people shopping around. If people want to invest the time, by all means do it. But I object to the notion it's as simple as getting a quote. Getting more options can in fact sometimes mean a bad thing if you switch from a proven-reliable product to something that is cheaper up front but worse later.
It's free, takes less than a half hour, and there's no obligation to purchase anything, it's just a quote.
Then one day while I was on the way to IAH to fly to Europe, an illegal alien in a stolen van (so no license, insurance, etc...) crossed the median and hit me head-on.
State Farm took care of everything. Ev. Ry. Thing. Even made sure I didn't miss the flight.
When I came back to America a couple of weeks later, my completely repaired car was sitting in their parking lot waiting for me. That's why I stick with State Farm, and am OK paying more than I would for "discount" insurance.