. . . wow.
Okay, let's break this down.
First off, they never attempted to initiate a stop, high risk, felony, or traffic. You do not deploy anything without first attempting a stop. That's just straight up wrong and they're going to be liable on that alone.
Second, you disable a car, permanently totaling it. YOU GIVE THE WOMAN AND THE CHILD A ******* RIDE YOU GORMLESS MINGER!
Third, the attempts by the city to avoid payment is just disgusting. This is where a decent attorney will own that city and whomever the bean counter or politician is that made the decision.
Fourth, yes, this was a training issue, but a mistake this major also demands internal discipline. Formal written at the very least. No one was physically hurt, but you're causing a lot of problems because you fucked up. That should be paper. Again, at the very least.
A lawyer is going to see that and reach out, dreaming of 10% of 6 figures. Tempe will pay. And they'll feel really bad they didn't do the right thing in the first place.