I don't know about you but one of the reasons I got a dog was to enjoy nice, leisurely walks. I would see people walking in the evening, strolling along, dog walking nicely beside their human.
Now  that I've had dogs for the past 14 years, I still see people strolling along after dinner with their dogs. I also see people being dragged along, dogs barking, lunging, jumping and otherwise behaving in a less than desired manner.

I live in a neighbourhood with lots of children, all ages and lots of new puppies. I love the idea of children growing up with family pets and of children learning the responsibility of caring for an animal. 

What I don't love is seeing young children with the family pet on leash and no adult supervising the interaction. Young puppies are very impressionable when you first get them. They are always making associations - whether good or bad.

Imagine this scenario:
3 or 4 young children, new puppy on flat collar and short leash. Puppy is doing what puppies do - pull, chew, dig, jump, bark, get over aroused.

Children, excited to have a puppy, are also aroused - yelling, shouting, screaming in high pitched voices, jumping around.
Puppy pulls to sniff something or is barking. The children are jerking the puppy's leash to pull him back along with screaming, jumping around because they don't know what to do as the puppy keeps pulling and getting more aroused.

Think of what the puppy is learning. All the new and different stimuli are now scary.  He is making lots of unwanted associations which will impact what he experiences for the rest of his life. 

It's no different than your first experiences of anything novel with a teacher - whether piano, dance, baseball, math, you name it. A good teacher will make sure the experience is fun and ensure you want to continue. Have bad teacher and you never want to play the piano or continue with dance classes again.

In my opinion, any untrained puppy needs to be walked by someone who can guide both child and puppy during this very important learning period. Puppyhood and adolescence have difference challenges. Both need the guidance of an adult so unwanted behaviour does not develop and desired behaviour is encouraged.