I have been in different big nature reserves in Europe. An unpleasnt common pattern I saw is that in all of them I saw signs saying that dogs must be kept on a lead, but nobody cares. That doesn't bother me. the few times I encounter a dog they ignore me, but the dog won't ignore the wildlife, several time I saw dogs chasing small animals. Once I saw a big dog running away to chase two deers. The owner, taken aback, didn't know what to do and didn't do anything else than try and call a dog that was gone and too far away to hear them.
The real problem I see actually is not the present, but the future. Dog ownership is becoming increasingly common and hiking trails risk being literally overwhelmed by barking dogs. Can we prevent it in some way?