Car insurance has long moved to trust but verify with repair shops. They let the shop assess the damage to your car, rather than sending their own adjusters. The adjusters they have are used to audit their repair shops and sanction or remove ones that are cheating.
The compensation to the shops is in the form of steering business to them from their agents when customers call and say they’ve been in a wreck.
They could do the same with tire centers. We offer a discount if you get tires from here or there. But I think the problem is that what those companies want to do is not change your rates except when you have a life event, get a new car, or have an accident. Tires would have your rates going up and down, unless they made a AAA type of deal with tire centers where you show your insurance and they give you a discount for the tires. Which perhaps could work.
I don’t know if it “certainly” would be cheaper for them to administer a program and maybe that’s why they don’t. It still takes manpower and maintenance teams to keep the program running and maybe that’s not worth enough dollars per year.
Also as we discovered from the Firestone/Ford debacle, a safe tire on one model of vehicle is not safe on another. So you have to do safety research on every vehicle and tire combo.