I have come across purely mechanical reasons that explain why children have piping/high pitched voices - length of trachea etc. However, I find myself wondering whether there isn't a deeper evolutionary reason why the mechanics evolved that way. Is there a Kinderschema type explanation for this? I have attempted to find information on the subject and turned up nothing - perhaps because I am simply not searching for the right thing.
Children have high pitched voices relative to adults because their vocal folds are shorter and physics demands that short vocal folds result in higher pitches. The format frequencies of children are also higher than adults due to shorter vocal tract lengths.
I think your question is, is there a speech communication reason for the vocal folds and vocal tract of children to be shorter than adults to which I would argue that it is unlikely. While it is possible to be grown with adult sized features (e.g., the inner ear and the middle ear ossicles), generally babies are smaller than adults. There would need to be a strong evolutionary advantage to being born with a really long vocal tract. Second, from what I can piece together, (e.g., this article) a shorter vocal tract is desirable for suckling. Therefore I would conclude that evolutionary speaking babies have shorter vocal tracts because they are smaller than adults and if the vocal tract was longer it would make it harder to feed.