I agree with everything you say except for two things:
I do agree with this one! - agreeing with 'no dogs allowed to be in the care of under 18s in public (obviously dogs such as guide dogs would be exempt).
Are you really saying that a sensible 14-year-old shouldn't be able to take the family's amiable toy poodle up the road to see a friend or for a quick run around the park? Yes, incidents can happen, but IME they are very rare even when walking in popular areas.
How would you regulate who can have a working dog? There are many many trainers out there training dog for protection work and bite sports, who have zero security work, military or police affiliations - how are you stopping them, they are a huge part of the problem.
Firstly - just for clarity, as I'm sure you know this if (iirc) you have lurchers etc - there is a very hazy dividing line between 'working dog' and 'pet'. I know a huge number of working gundogs, and I've seen a fair few lurchers, some of them enormous, and most of them living pet lives. Some of these dogs are enormous. I've yet to meet one who was a threat to a person.
Secondly, I would argue that bite and protection sports are not part of the problem. See here https://dogtrainersaustralia.org/wp-content/uploads/2024/06/PDTA-Submission.pdf for a reasoned discussion. If there is evidence that there are people training protection where the dogs turn out to be a problem, then perhaps regulate that kind of training. The protection sports (and protection sport breeding) feed in massively to police and military working dogs, to the point that without the 'hobby' people, the breeding lines could easily become unviable. Developments in protection sport training (the use of play, for example) have changed training for the actual working dogs.
It's also worth pointing out that people who belong to dog clubs tend to have pretty high standards for their dogs and aggression, to either people or other dogs, is viewed extremely dimly, and the dog is likely to be banned from future events.
Other than that, you make a lot of excellent points. You're spot on about dog parks - IME popular dog walking places are an absolute magnet for people with dickhead dogs. There's one I go to sometimes (it's a great space for dog training if it's quiet, pitches, scrub, woodland, fences to jump...) and there is a small dog there who I avoid like plague, esp if he is off-lead - as he all too often is. Same place, there used to be a poodle with a bite history.
I also agree about assistance dog. Locally (again) I know of a dog who was trained by her owner and a dog trainer to assist in various tasks. Perhaps the KC could do something useful and assess self-trained assistance dogs for a nominal fee...
ETA, crazy that your fall down the stairs went down as a bite. One of my DC fell over the dog and needed stitches - perhaps that went down as a bite as well! (The dog was a good as gold about it!)