@kc431 that argument doesn't quite work. We all know what is being licensed when you acquire a driving license - responsible driving behaviour. A license can only be acquired after you have a sat a test to show you can drive competently and you can lose your license if you either drive dangerously OR you fail to meet an objective standard which suggests you might drive dangerously e.g. you develop a medical condition which causes loss of consciousness or sight loss. In any situation where you drive a car without a license you are committing a criminal offence, easy to check by the police. It's true the law gets broken a lot but its easy to see a) why it is a good idea and b) how it can be enforced and is therefore a deterrent to non-licensed wannabe drivers. The difficulty with a dog 'license' is that showing everyone why it is a good idea and enforcing it are both hard. E.g. are you licensing that someone is a responsible dog owner? Or that they have just some minimal knowledge of animal welfare necessary before acquiring a dog? Mandatory training for dogs isn't like driving. Dogs are specific i.e. you build a relationship with one dog. I have a trained collie, but no idea how to handle my neighbours Jack Russell. In fact people thinking they can 'drive' dogs in general is a big part of the problem.
And once licensed how do you enforce it? Do you have strict liability that only people trained on that dog can walk it outside the house? Or is there a class of other professionals? Whatabout wider family members with whom the dog has a relationship? Can they all be licensed? There are some over the top suggestions on this thread re dogs never being walked off lead or without muzzles which I appreciate come from a place of fear which is understandable given the events of this year but disproportionate to the level of harm shown by most dogs. The difficulty with making licensing restrictions too stringent is it won't get popular support - which means in a country of dog-lovers a) it would never get legislated for and b) even if legislated will end up being the kind of minimal mandatory training requirement (watch this online workshop) which I fear could be worse than useless.
Don't get me wrong I am absolutely in favour of training for dog-owners and think it is irresponsible dog ownership not to get training advice. I have gone to a lot of training classes myself and would say whenever you get a new dog go to classes or get a trainer involved, even if you have done it all before lots of time, each dog is different and there is always more to learn. But I don't see the driving training metaphor mapping to dogs.
Mandatory training after any event - dog getting loose, dog bite, dog causing excessive barking - is brought to the attn of the police or local authority is sensible as at that point you have an owner with a motivation to do some work and like a speed awareness course there might be engagement.
Licenses just to ensure the owner knows they have duties to the animal add little to the duties all pet owners already have under the Animal Act. The law as it stands just isn't enforced well, but in the era of the internet we don't need a license to bring to people's attention the minimum level of welfare needs dogs have. People aren't keeping their dogs chained up outside or failing to exercise them out of ignorance, but indifference. Like any animal lover I would love to see the current law more severely enforced, but the small number of prosecutions taken against the large number of cases of abuse is because the police don't have time. That said perhaps if people could see how closely animal welfare and human welfare is aligned and if we prosecuted abusers more harshly we might deter some of the outcomes (distressed dogs, poor breeding) which increase the risks to humans in the future maybe public support for prosecutions would grow - this isn't just about saving ickle puppies, but also ensuring people don't unwittingly buy reactive, anxious dogs as pets, or that neighbourhoods don't live in fear of neglected, aggressive dogs who want to escape their conditions.
That and everything @WiddlinDiddlin said.