No, then decent cops would leave, and we'd be left with jerks who have low job-mobility (no other skills), but are adept liars who can cover their asses when they get near trouble.
Most police officers already are jerks with low job-mobility - but I do think a framework where the department suffers for an individuals actions (and not the taxpayer footing the bill) would have a positive feedback effect.
If another officer's indiscretion or negligence were to reflect on your pay check, you would be less likely to help cover it up or ignore it.
I think I'd prefer the idea (I forget where I first saw it) that officers have to buy a bond/insurance. That way the worst ones would price themselves out of the market. Having group rates for officers/departments might have the effect you're looking for. I don't mind it terribly that local taxpayers have to foot at least some of the bill for this kind of thing. Hopefully they will be reminded come election time if a sheriff or a mayor has allowed deputies to run rough shod over peoples' rights.
We tend to cheer for social justice against government abuse of power, but we're always the ones footing the bill.
Settlement and damage costs should come out of the agent's salaries across the entire organization.
Maybe police officers will stop shooting black teenagers if everyone on the force is docked $5000 for each application of lethal force.