The issue is that for every good dog owner who trains their dog, puts it on a leash in public, picks up the dog shit and makes sure their dog can’t cause trouble, there is also some idiot who got a dog on a whim, mistreats it and doesn’t train it at all.
And most often the people who don’t care for training their dog are also the people who don’t care to secure the dog in public places.
I know that’s a generalisation and there probably are some counter examples. But a “don’t care” attitude generally runs through everything a person does.
And having a dog is a multiplier of what trouble that “don’t care” attitude can cause.
That’s why I am for licensing/inspections. For someone who does care it probably won’t change much. They already go to a training course with their dog. Just give them a license for completing the training/make that training mandatory if you don’t want to call it a license.
Any reasonable dog owner will be at vet in regular intervals anyway. Just let the vet not only check whether the dog is physically fit, but also if it obeys it’s owner and if it shows signs of abuse. And make that checkup mandatory. It’s better for the dogs anyway if they get their health checked regularly.
I see why you think it’s not necessary, because you might be the kind of dog owner who cares and then it’s just additional hassle. But, as I said, there are many who don’t care, even if in your bubble (and I don’t mean this word negatively) everyone cares for their dogs.