Leashes do two things of concern to dog owners: 1) they limit the dog's space and speed to human limitations, and 2) they get tangled up if two dogs are playing.

To explain more:

Dogs NEED exercise. An off-leash dog is free to sprint and leap at will --- for many dogs, this means a level of exercise that humans just can't keep up with. The cardiovascular effect is great for the dog's longevity and weight control, and the overall effect (endorphins? who knows?) makes most dogs calmer and better behaved at home. Neurotic activities such as destructive chewing, nuisance barking, separation anxiety, and overall obnoxiousness are definitely reduced by regular, intensive exercise. Ask any dog owner or trainer. These effects are so well known that they hardly need further proof.

Dogs also NEED social activity, with other dogs and humans. Social activity gets them used to everyday life. A socialized dog is much less apprehensive, tense, scary or nutty, so playing with other dogs is one of the most important opportunities an owner can provide for the dog's, and the owner's, peace of mind.

It's true that it is technically possible for dogs to meet other dogs when on a leash, but leashes get in the way of any kind of play or complex activity. In fact, a leash can have a negative effect --- entanglements and constraint can teach the dog to be anxious about social dog situations.

So, the bottom line is that having dogs off-leash, in a safe way, has lots of benefits that can't be achieved otherwise.