"Yes of course they do Tabularasa. They drop whatever they are doing and they do their best to intervene, given their own physical condition and their perception of the danger their child seems to be in, if they see what is going on." So why have you spent pages arguing that supervising children is unreasonable?
There is no contradiction there Tabularasa.
Parents supervise according to the level of danger they perceive to their child, not to the dog, and dog owners have no right to expect them to supervise one ounce more than what they feel they owe by way of supervision or protection to their own child.
As far as rudeness goes, many feel if you are going to bring an attractive dog into a park you are asking for whatever attention comes your way. If you don't want the attention, don't bring the equivalent of a Victoria's Secret swimsuit model out to the place where its natural fanbase congregates.
It's been repeatedly said that dog owners aren't expecting some extra level of supervision because their dogs are dangerous, just the normal amount that parents use to stop children being a nuisance to other people who are going about their business in the same public space.
And that is where dog owners are failing utterly and completely to understand the problem here. Parents are attuned to danger to their own children. If you and your dog (together, the pair of you) do not look threatening to their child then they will relax a bit. As I suggested, a dodgy looking older man in a park with his dog is much more likely to raise the hackles of parents than a woman out with her pet.
If you, the dog owner, are happy to bring an attractive pet whom you consider well behaved out among children, then parents can't be blamed for thinking you must be happy enough to have children express admiration for your dog in their own way or that their children are safe enough to allow them to approach.
You are bringing it out to a place where small people who love dogs gather. They are going to beg for a dog all the way home -- you do not seem to realise how much children want dogs.
This combination of parental perception of danger or lack thereof plus children's attraction to nice looking dogs plus your insistence on going out when children are out and to places where they go to means you bring much of your discombobulation upon yourself by your choice of place and time for a walk.
It's not about finding children approaching so unbearable that I should avoid them...it is a very minor irritant and my annoyance is directed at the adult who is either not supervising the child or doesn't care enough about their child's behaviour to stop them being rude.
Children are rude. Get over it. If they weren't poking your dog they would be poking other children or taking their toys, which they also find fascinating. Or they would be trying to catch squirrels or pigeons. If you brought children to the playground sandpit my children used when they were small you would learn from your first experience to leave the fancy spades and buckets at home and use recycled, cut up plastic junk - detergent scoops and containers and milk containers - as digging equipment. This is because the one thing you can count on with children is immaturity.