> So my theory is as well that some of these words derived from their use by infants when they desire attention or breastfeeding and were not “invented” by adults.

An addendum to your theory. Words with few short syllables, composed of vowels and labial consonants are probably the easiest to pronounce, therefore "independently discovered" by babies. They are not "invented" by adults in a sense that "hey let's use this word for this phenomena", but rather "assigned" in a sense that "the baby babbles this, so let's refer to this phenomena by it". I guess this process is similar to how onomatopoeias appear in languages.