I don't think it's workable. I also don't think it will achieve a reduction in bites or welfare standards
Things like car tax are workable because of cameras registering number plates and because your car is parked outside your house. How would you know who is registered? How would people be found?
As some that works in animal welfare, you absolutely should not enforce this in a way that impacts welfare. We should not be doing anything that encourages people to avoid vet care. Theres a reason the nhs doesn't check citizenship before treatment.
Anyway dog bites are massively more common in the home, dog bites to randomers not known to the dog are uncommon. So placing scanners say at parks are unlikely to do much
What will happen is people with unregistered dogs, will be exercising them less, potentially hiding them away in houses (if you found a way to enforce it outside), and dogs that are unwell will be hidden from vets.
This will lead to a decrease in welfare and a higher likely hood of incidences
Things like ear cropping are illegal in this country but are plainly done frequently because the set of people that probably most need this legislation are the people least likely to follow it. It's like microchipping, the dodgy owners still don't and the people that do are generally following rules anyway. Ear cropping you can visibly see but still it's rarely enforced.
Since the law on microchipping, there is a legal register of every single dog. Just by doing this, it doesn't improve welfare or safety. In the same way car tax doesn't cause less accidents but an mot does.
What is actually needed is dogs to be able to live in suitable environments, be matched to the their homes and be regularly health and temperament checked. I have zero idea of how you'd do home checks, or checks on every dog.