I do not think it is as difficult as that. I think it is quite easy. There are plenty of parks nowadays with by-laws that say you cannot take your dog into the park or you have to have it on a lead or whatever. These proposals will make that kind of rule much easier.
It would be possible to look at the question of whether the access itself was fundamentally different from many other things. On the other hand, having thought about that, do you really want an annual or three-yearly review of ordinary gating orders in back streets which are completely non-controversial? I am sure it is possible to think of a way through this and to find a solution.