A full ban of any bully type breed - Whilst I think I understand your point, the fact is Staffies are incredibly highly recommended as family dogs but fall within 'bull-breed' under many criteria, as do things like Boxers which again are well-known and well loved family dogs. So this wouldn't work.
A maximum weight restriction for any domestic dog - St Bernards? Bernese? This wouldn't work
Restrictions on which dogs can be domestic pets and which are for work only e.g., Rottweiler only for police dog handlers - Disagree. I have a friend who owns a Malinois and it's probably the happiest, well-adjusted, dog I have ever met. It's certainly happier than most 'family' pets I know.
Restrictions on size of dog you can own based on the size of your property - Some of the biggest dogs require smaller properties. Greyhounds are large, for example, but can easily live in flats.
A mandatory training course for new dog owners - Just wouldn't work and a waste of everyones time. What would be better is restrictions on first time owners owning particular breeds - and in that I include Golden Retrievers, GSDs, Springer Spaniels, Border Collies etc.
A return to licensing with a points based system for infringements - And how will this be financed? Everyone is already at breaking point tax wise.
Ultimately, responsibility will always (for financial and practical reasons) need to lay with the general public not being complete tossers. And as we have all seen repeatedly over the last few years, people are tossers.