Rosebud, it simply wouldn't work for a huge number of dogs.
If you have a dog with any kind of training need (puppy/nervous/over-excited/dog-aggressive - note I am NOT including human-aggressive here) then one of your key weapons in training is by using rewards, and your two biggest rewards (besides voice, attention etc) are food and toys.
So if you only occasionally allow dogs out of their muzzles in small, crowded, dog 'corralls', then you would have a lot of dogs with potential behaviour issues, all pent-up with frustration at not being able to do their normal dog behaviour of sniffing and licking things in their environment, confined in together.
If I'm throwing a ball for my dog in a park and you walk past I know he won't approach or bother you, because the ball game is more fun than a random stranger. If you have young children or another dog with you, I'll call him to me, and I taught him that recall using toys and treats which go into his mouth. If you insist on a muzzle you're going to make training virtually impossible in public spaces. And dogs have to be trained away from the home as well as in it, because they don't automatically make the connection that the same rules apply everywhere otherwise.
Training can be time-consuming and frustrating enough, insist on muzzles and a lot more people just wouldn't bother. End result - more out of control, poorly trained, poorly socialised, potentially aggressive dogs.