There are also apparently canvassers paid by the county who go door to door checking for this?! I'm not the kind of person to typically nitpick about where my taxes are going, but...I retroactively and broadly apologize for every lighthearted jab I may have ever made about TV licensing in the UK. This is beyond dumb in comparison. And my condolences, the fact that this system leads to them harassing you in this way is completely insane.
A dog can be a public health threat, in both terms of disease and attacks on people or other dogs. Many states require rabies vaccinations for example .The owners are ultimately liable for that and there should be a way to track that.
Plus the fees frequently fund animal control and shelters in many areas.
In theory the fees for car registration go towards maintaining the infrastructure that cars make use of. Taking a dog out in public doesn't have many similar externalities, and there are already targeted fines for off-leash dogs or for failing to clean up after them. I live in an area with a decent amount of dog-friendly public infrastructure, but that just seems like it would fall under regular parks funding, and I don't get a bill every year asking me how much time I spent at the park.
As far as where the funding goes, I'm sure that could be done better. Everyone in the county benefits from funded animal control and shelters. By adopting my dog from a shelter I have actually reduced the burden of responsibility on the local shelter system, which then seems backwards to tax me for.
Registration + annual fees aside though, door-to-door dog inspections are where I would absolutely draw the line. That we have any room at all to fund that is crazy to me.
Unless a new breed has been named, or an /s was missing, I'm not sure they will be very successful in their recovery attempts.