a 'public place' is anywhere the public have a right to be.
This includes your front garden (where there is an implied right of access to your door to deliver, to contact you, to come in and rescue you), and inside your car (ditto the rescue bit, not so much the delivery bit).
Realistically, people are going to fall foul of a strict lead and muzzle rule most commonly in remote rural areas, and in their own garden and car.
Where do you think the law would be policed most often and most practically?
Do you want a huge fine and criminal record because you took your dogs muzzle off whilst they were being car sick? Do you think that will be effective in reducing dog related attacks and fatalities?
I pick that example as this is how one owner of a exempted (ie illegal breed that has been through the court process to be added to the exempt register. Ie. a dog of a particular breed who has been proven not to be a danger) lost their dog - they took the muzzle off in the car so because she was vomiting and choking on it. They were caught, she died, they were fined.
Lead and muzzle laws will punish responsible owners and happy, healthy dogs who are not particularly a risk to anyone.
We have not got the infrastructure, the police presence, the specialist knowledge or the time, or funding, to create new legislation like this, and apply it in such a way that the people causing the problem would actually be impacted by it.
I'd like microchips to actually work, ie, one database with strict controls over who can edit it and information CANNOT be removed from it, ever.
Then an ownership trail can be formed from breeder to owner to owner and so on.
Then new legislation - if your dog is involved in an offence, you and everyone else in the chain of ownership are potentially liable for that, with diminishing responsibility as appropriate of course (so if you bred a nice puppy, sold to nice owners, can show evidence for this.. but then the wheels fell off their life and they died and the dog went to a rescue... you're in the clear. But if you sold on a dog you knew to be dangerous, to a family with no dog experience and lots of small kids... you're also in the shit!)
THAT would sharpen minds about both breeding and selling on/rehoming.
However we do not have that single database, currently chip details can be altered by a wide variety of people, chips fail and chips move and we have no way of forcing people to have puppies chipped before moving to their new owner (despite it being law that they should be).