It can be selfish and antisocial.
If you smoke, you’re selfish because your eventual healthcare needs - caused by your own habits - is funded by the rest of us.
If you have a dog, and it makes a mess on public property (piss and or shit) - you’re selfish because cleaning it up is funded by the rest of us.
If you smoke in a crowded room, your unpleasant smoke & discarded cigarette butts cause an actual risk / hazard for the rest of us. Antisocial.
If you bring a dog into a public place, you impinge on those with allergies / fear of dogs, the dogs run up to people unsolicited and cause trouble, and in some cases cause injuries. Antisocial.
So stricter controls would absolutely help mitigate these negative externalities borne by non-dog owners and funded by us all.
I agree that mandatory training would be difficult but it could be a multi-level thing, with level 1 basic being mandatory, proceeding to voluntary levels 2-6.
Dogs could wear QR codes on their collars / muzzles to allow anyone to check their last training course, with badges or whatever to proudly show what good boys/girls they are for having completed the more advanced courses.
This is absolutely not unreasonable - a fairer way to impose dogs on wider society.