OK, so I think the solution is for trail centres to introduce the following:
Clear rules on where you can and cannot take dogs - my suggestion would be green cycle trails and shared pathways only, not MTB trails.
The ability to fine people who do not obey the rules and who take their dogs on trails where they are not permitted, as is the case if you take your dog into a children's playground or other place where they are permitted for safety reasons.
Draconian? Maybe. But as a dog owner, I am responsible for the safety and wellbeing of my dog. He goes where I go, therefore I should be ensuring that the places I take him to are not a risk to his safety. I don't let him off the lead near any traffic, for example, so why might I put him in danger of being mown down by a mountain bike? I put him on the lead near children or other dogs who are on the lead, partly out of courtesy, but partly because I know that in that situation I can't guarantee his safety. A small child who is scared of dogs and has not been taught how to behave around them might react by lashing out and hurting him. If I see another dog on a lead in an area where dogs are allowed to roam free, I must assume that dog might be aggressive and therefore I need to be able to stop him going into a situation where he may get hurt.
A dog owner who is prepared to risk their dog's safety just for their own convenience or to make a point about being able to go where they like with their dog is not a responsible owner IMO.