Perhaps we should say that anyone unaccompanied by children should also be denied access to public places since....oooh,....I don't know.......they could be a predator? 
Or perhaps we should say nobody should be allowed to procreate because adults abuse children in their own homes?
Geez, I feel embarrassed even writing those things but you are being ridiculous OP. Where I live there are no "dog only" areas so basically I would have to keep my dog leashed at all times, even when I know that on average I bump into all of about 4 people on an hour's walk through local public woodland?
My dog is a 14 month old puppy (yes, still definitely a pup :o ).
If she is walking along the road I keep her on her leash. Ditto a public park with a children's play area within it. Unless of course there are no children there, in which case I let her run free. The instant I see a child appear, I leash her. Not because she is dangerous but because she loves everyone and thinks everyone loves her
.
She is a vizsla and therefore a medium/large breed (almost as tall as my 6 year old) and I understand how intimidating she potentially could be to an adult, never mind a small child.
Even as a dog owner, I dislike other people letting their dogs approach my DCs without any kind of warning, and warn DCs to be responsible and not approach other dogs. This is the message non-dog owners should be giving their DCs, rather than "oooh go and stroke the nice doggy" because possibly the "nice doggy" is in a bit of a strop or is, in fact, scared of small people themselves.
If we are walking through fields or woodland she is free to run. HOWEVER, again, if I see a parent with children I will tend to leash her because when she is running full pelt she could bowl over DH (and he isn't exactly light weight :o )
I would not even consider letting my dog off the leash near children if she had any history of aggression or if she didn't have good recall.
The people you are talking about are a very small percentage of dog owners, ime.
Am now going to pour myself a
and breathe deeply......