Dogs in NYC are already required to wear tags with their rabies vaccination statuses and IDs. That also isn't really checked, but it absolutely could be by simply stopping people walking their dogs and requesting to see their ID tag.
Come on, you can't be serious. Police and code enforcement officers aren't going to stop random dog walkers on the street to demand DNA test results. Real Americans don't tolerate that kind of government overreach, and the authorities already didn't even have time to investigate actual crimes.
I didn't say they are going to, and you didn't say they wouldn't. You said they couldn't (because people "would just ignore it") and I said they absolutely could. Which is true.
Re "Real Americans", get a grip.