Not likely. But it does contribute to a breakdown in the relationship between police officers and the citizenry.
What would likely happen, in the end, is that the police could need the assistence of the publics on something, or an overwhelmed officer could find himself in trouble and they’d find nobody willing to intervene.
I like the idea of social ostracism and shunning, for starters. When animal control people are available to handle any dog, the current SOP is morally indefensible and they know it. They’re not doing this @#$!! because they really have to, they’re doing it because they can and want to, and will have the system behind them. Make the “family pet killer” label stick on them, and isolate them and their families from the community and the company of respectable people.