I think all dogs should be on a lead in public regardless of whether the owner believes them to be well behaved or not. A large area of woodland locally is now virtually a no go area for the general public due to dogs running free and no sign of the owner(s).
Dog excrement left on paths or worse still, in plastic bags just lobbed into the undergrowth.
Our local Facebook page regularly has pleas from owners who have lost a dog, last seen "chasing a deer" or running free in someone's field. They are a d**n nuisance.
I know there are many dog owners who are responsible and careful, but there are a heck of a lot who treat their pets as child substitutes and expect the rest of the population to feel the same adoration as they do.
Taking your dog, on a lead on a public path across a field is fine. Allowing your dog to run loose over land that does not belong to you just because you feel it needs it is not.
No I'm not a dog hater. I have had dogs in the past but no longer. My dog was exercised in a farmer's field with his permission, provided no livestock was there, otherwise it was a nearby park, on a lead or in my own (small) garden.
In my view, if you feel your pet cannot be exercised adequately on a lead in public or loose on land that either belongs to you OR where you have the permission of the owner, then maybe you out to reconsider whether you should have a dog in the first place.