In my experience (I sued my town for violating my first amendment rights), the city will have insurance that will cover any damages or settlement they have to pay. Their premiums will likely go up, but the impact to taxpayers is probably minimal.

Perhaps in the first order, but when premiums go up and go up across all policies due to the acceptability of litigation... Everyone pays eventually.

Its a bit like saying driving dangerously is OK because you have insurance. Until everyone drives dangerously and insurance is sky high for all.

That said, they should be sued.