I don't think the original poster is being unreasonable at all.
If the signs say dogs are to be on leads then they should be on leads. There are too many people who don't follow rules these days.
I have a rescue Staffie from Battersea who was badly treated before she came to us and is very reactive to other dogs if they approach her, for this reason she is always on a lead. Far too often other owners allow their dogs to run up to her calling out, "They're friendly!", well mine isn't and she will lunge and bark if afraid. These people rarely have good recall for their dogs. Dogs are meant to be under their owners control and having your dog off the lead with poor recall skills is not having them under control. I have spent years and a great deal of money on a behaviourist trying to get over this issue, she is better now, but I think the problems are so deep rooted that she will never get over them.
Not everyone likes dogs, they don't want dogs running up to them "to be friendly". If I was with children I would be very wary of any approaching dogs regardless of size.
I had an incident in the car park of Scotney Castle last month, we were walking to the fields, when a woman let her gundog (pointer type) out of the back of her car not on a lead, the dog ran up to us, very big and bouncy so my dog reacted by barking, I did call out to the woman that my dog wasn't friendly but her dog was out of the car and bouncing around before she could stop it. She struggled to call her dog back and gave us a very judgmental look as if was our fault, maybe due to my breed of dog. Yet another person ignoring rules as dogs should be on leads at National Trust properties, also very dangerous letting your dog out in a car park not on a lead. This dog could have easily knocked over a child or an older person or someone with mobility issues.