My point was not so much that babies don't sing, but more that the discussion might be more interesting if one could separate spoken language from music just for the sake of this discussion. Now I suspect explaining why I think so is gonna be a bit difficult and ultimately fruitless
I personally am still of the opinion that music piggybacked language (noone's provided a good counter argument that I've seen) and so I personally don't find it weird or contradictory that language and music is mixed in our evolutionary history. But anyone making an argument that musical skill has started to become a distinct trait from language which is being selected for on it's own terms may find it useful to have a way to describe that music with a definition that does not automatically include normal language which, as I wrote, all adult healthy humans are capable of.
Anyways, I'll leave that discussion for them.