The reason why dog owners only rarely control their dogs on shared use paths (let alone put them on a short lead) is because many clearly think that cyclists should not be there (even if technically allowed), therefore why should they consider how they might inconvenience cyclists?
Various comments in this thread (and/or maybe others of late) are suggesting that dog owners are not supposed to let their dogs off their leads on shared use paths, or if they are off the lead, then the inference seems to be that the dogs much be kept "under control" to the extent that they are beside their owner, walking to heel, 100% of the time.
As a dog owner myself, I'm confused by these sentiments. Maybe I'm misunderstanding the points being made, but this is the way I'm reading them. And to be perfectly honest, I'm confused, because I wasn't aware of any kind of law or rule that said I can't let my dogs off the lead on a shared use path and let them run around.
If a cyclist is sharing the use of the path, that's fine, but who is to say that the cyclist has priority over the dog and/or its owner? I come across dogs regularly on my daily commute on the cycle path from Ocean Terminal up to the Red Bridge, and many times I've had to brake suddenly because a wayward dog has decided that they want to play with my front wheel. That's life - it's a shared path, I don't have more rights than the dog and the owner. I simply avoid the dog, and continue on my way.
But then, I could be missing out on something. Maybe there's some rules in the Highway Code or something similar that makes it clear that this shouldn't be allowed?