Having hands plus less of or less good neural hardware means less dominance, as we see with our simian cousins, yet having the greatest brain on the planet wouldn't provide dominance without the ability to fabricate things.
It also doesn't seem to be achievable with on the fly statements, only memorized oration. Notice how my citation interestingly shows that the 39 bits per second isn't a count of syllables, but of semantic information. Some languages have faster, simpler syllables, but the overall information bandwidth flow ends up being the same. You probably can bypass that 39 bit with practice and memorization, essentially applying higher level tags to large bodies of what you're saying via practicing repeated phrases.
That seems to prove where the bandwidth constraint is, on the stream out side.
https://www.sciencemag.org/news/2019/09/human-speech-may-hav...
It makes sense that other animals may be able to cargo cult some of the underlying mechanical representations of speech, but would lack the neural hardware that propelled us to dominance on the incredible short time spans of human history and prehistory.