Yes they would, but the flip side of them not being able to price people based on actual driving behavior is by charging all men higher, all single people higher vs married people, and poor people higher based on credit score.
Plus why single out insurance companies and ban them from creepily tracking you wherever you go and not all the other companies who do that with your cell phone.
Also to be pedantic, the don't want to put trackers in the car, that is expensive. They want to use your cell phone like all the other apps tracking you, or they want the car manufactures to let them in on their data since most modern cars have the ability to track and broadcast location.
>made a claim where I was at fault.
That's a big caveat. There are plenty of accidents that are truly not one parties fault, but according to law even being judged as 49% at fault is still "not at fault". And even in cases of 0% at fault as determine by the insurance adjusters, theres a big chance one still had contributing factors.
Also, there's a big chance not at fault claims will be taken into account when pricing you and raise your prices. Just right??
On the other hand, not at fault accidents do correlated with higher risk, and it's easy to see why. For example, people who get rear ended are not at fault. But following the car ahead too closely leads to needing to brake harder, increasing the chance of being rear ended. Following too closely also increases the chance of rear ending the vehicle in front.