Or mama for "father" in quite a few Oceanic languages. The Anglican Church
has used Mama as a title for (male) priests in Vanuatu and the Solomon Islands.
What we can reasonably infer from the evidence the two French authors
review is that infant babbling was probably similar some tens of millennia
ago to what it is today; and that adults have, for a long time, made
words out of their children's vocalizations. Usually these words remained
in the baby-talk register, but sometimes they found their way into
grown-up language. The fallacy is to conclude from this that these words
have come down to us by continuous inheritance from proto-human. They
are created anew here and there, now and then, and once they become real
words they can change and be lost like any other. To show that they were
part of the proto-vocabulary, you would have to go through the same
type of argument as for TIK and MELG and the rest, and run into the
same impasse.
It surprised me, during one of the previous rounds of this argument, to
find that "mama" and "papa" are not attested in English before the 16th century.
They are clearly borrowings from French, and latterly other European
languages (Italian, Yiddish, etc). Before that, English of course had
"mother" and "father", from PIE *mā and *pə, fitted out with IE morphology.
I don't think Latin mamma 'breast' has any strict cognates, so it's
probably another independent creation from the same mine.