I’m not sure why we would care about controlling for price of the car…

There are many reasons why one could be interested in that.

On the personal decision making level you might want to know what car provides the best safety record for your budget. If you can afford a tesla you would be interested in the safety of similarly priced cars to compare with.

On the society wide statistics level Tesla drivers are not exactly like the whole driving population. If for no other reason the price selects a specific demographics with their associated behaviour patterns. By controlling for the price we can hope to better control for these differences too.

You’d also want to control for age of car. Recent expensive cars are more likely to have advanced safety features that older or cheaper cars lack. Maintenance can also be a factor.

Price indicates class of the vehicle (premium in Tesla’s case), so they can be compared with cars in the same class that have similar safety features.

What were the numbers, out of curiosity? Telsa is worse per mile for safety than others similarly priced cars?

I don't remember except that i found it significant, i tried to find the article i think it was a university that did the study, if i find it i will post it.