I'm not going to go so far as to say it's a fact, since there are few or zero very primitive languages around today that haven't interacted with other languages, but I would guess that most languages, including primitive languages, have more nouns than command verbs and would hence be dominated by multi-syllable words (especially if having a longer name somehow carried prestige). Whether that's actually true or not is irrelevant.
It is relevant that nouns and verbs are processed differently by different parts of the brain. (
Verb and Verb-Derived Noun Production: Hemifield Similarities and Differences is one example, chosen only because you can view at least some substance without having to pay a fee).
There is some range of randomness in actual sounds for a given word ("give" vs "sit" for example), but the development of language has some serious constraints that keep the language from straying off "randomly". The same type of patterns keep popping up over and over (even the "so bad it's good", "so pleasurable it hurts", "laugh so hard I cried" pattern).