Simple registration I have less of a problem with for some of the reasons you listed. Cross-reference with vet records, have fines specifically for missing rabies vaccinations etc for the sake of public health, sure. Maybe even bill me a nominal paperwork amount for the initial registration, maybe waive it for adoptions or make it an automatic thing the shelter does and builds into their fees. Having an annual subscription to my own dog is what seems ridiculous.

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.