Yes, the fact that children 4-5 years old skip more because it is less fatiguing than walking is part of an evolutionary cycle. As these children get older, skipping becomes more fatiguing than walking so they begin to walk more. Less evolved mammals such as kangaroos hop or skip regularly because this is less fatiguing to them than walking.
It requires more energy and more work to skip than to walk as skipping requires little bursts of energy and walking is a continuous use of energy. Think about it, try running 1 mile, jogging 1 mile, and walking one mile at separate times. With running and jogging, you'll get to your destination quicker, but at the cost of energy expenditure, however, with walking you maintain your energy, but at the cost of time. This can be related to the topic.
Skipping may be the sign of modern times, but I do not believe it is a sign of evolution path for humanity. Before we jump to such far-fetched conclusions, perhaps we should investigate here and now. Maybe the reason why the children prefer skipping over walking is that they are more agitated and restless then previous generation of children, and this is their way of coping with that. Whatever the reason may be, let's not pin it on evolution just yet.
Since this deals with something that can only happen sometimes and is not proven to always happen, it likely has more to do with psychological tendencies in children. Children 4-5 years old generally care less about public appearance and care more about the fun or feel of the activity (or they may just be unaware of those things) than older children or adults, making them more inclined to skip.
Children 4-5 years old tend to skip more because it is less fatiguing than walking. I do not believe that this is a part of our evolutionary cycle. Walking to children is so boring, skipping is more fun, and it is just like running, except running is close to walking. Everyone should skip now and then.
I agree that galloping and skipping is an evolutionary cycle but I believe the cause of this galloping (skipping*), has one purpose at that particular age and that is the bodies way of improving ones motor functions, to prepare for more complex movements.
I also have to disagree with the statement you made that "it is less fatiguing than walking". I must say that it is more efficient to walk then gallop or skip as you put it . I will take a quote from Journal of Experimental Biology:
"Gallop is, though rarely used, a familiar gait for humans,".The obvious factor is because it is to costly on the body and the reason it is so familiar i believe is the fact that it helps us improve our motor skills. Link is below