I think yodeling, which often leaps from low notes to high, is partly inspired by birdsong.

Yes, sometimes we encounter birdsong in human music, but birdsong presents some problems.

1) the intervals fall "in the cracks of the piano" and can't be duplicated or notated in the usual way

2) Birds have two voice boxes while we have only one, and birds can produce some seriously complicated sounds.

3) The timing doesn't mesh with our system of a beats and measures.

4) Still, there are sounds that could imitated, such as the chickadee's "sad call" or the call of a whippoorwill. The reason composers don't use them is that other composers would ridicule them. It's fatal not to be earnest.