There's quite a few reasons
It won't decrease fatalities
Fatalities pretty much exclusively fall into the following categories
- A member of the dog's household (majority of cases)
- An guest invited to the dog's household
- A few cases of escaped dogs that have attacked the neighbours
- A couple of cases of dog professionals
I can't find a single modern case of a dog launching a fatal attack on a stranger while on a walk
https://en.m.wikipedia.org/wiki/List_of_fatal_dog_attacks_in_the_United_Kingdom
Exercise
Dogs normally cover far more distance than their owners do on a walk - they're here there and everywhere, and they need to run, especially when they're young.
If dogs are on leads then they cover far less ground and at lower speeds than they do off lead.
The result is that dogs don't get enough exercise, start to go stir crazy, and that's one way behaviour problems can start.
The next thing you know, you've got underexercised dogs cooped up at home with small children - not a good mix.
As the saying goes, 'a tired dog is a good dog'.
On lead interactions are much more tense and likely to result in conflict
This is for two reasons
- If you think in terms of fight Vs flight, dogs who are off lead know they always have the 'flight' option up their sleeve if required, so are less likely to opt for the fight option. Dogs on lead are acutely aware that they cannot just walk away and so will opt for fighting far more readily.
- Being on lead prevents them from displaying the full range of polite dog body language, including calming signals.
For instance, it's polite for dogs to approach each other on a curved trajectory. Running directly towards each other in a straight line is really very impolite - but that's exactly the trajectory two humans will choose if walking their dogs towards each other. This gets an interaction off to a bad start instantly!
Many dogs are a bit snappy on lead and lovely off lead.
Muzzles
Aren't a panacea - dogs can still do damage with them on by punching. They also prevent dogs from playing fetch and exhibiting breed-appropriate behaviours. For instance, gundogs (spaniels, retrievers etc) are bred to carry things around in their mouths. Preventing dogs with zero issues from doing that seems deeply unfair.
Very strong dogs
like XL Bullies ultimately aren't really controllable even if they are on a lead. They can drag their owners around and there's not much they can do about it.
Overall having dogs on a lead and muzzled would save a few picnics from being snaffled, but it wouldn't save any lives and it would likely increase fatalities overall.
We need evidence based policies, and a blanket lead + muzzle policy just doesn't stand up to scrutiny.