There is, however, a purpose to using baby-talk with infants. It just shouldn't be used with children as they get older and have already developed their language skills to a certain degree.
How many "baby-talkers" do you know speak slower or more repetitively? Most babble quickly and in a high pitch.
At least, that's been my experience with what people consider to be "baby talk". Speaking slower and more simply / repetitively with infants seems to be essentially the same as speaking "seriously" with them, as you don't use complex words or phrasing with adults starting to learn your language, and you deal with them seriously too. (or, you should be)