This is pure speculation: I suspect our ancestors used music + simple words for communication long before we evolved modern human language. Although language outstripped music in terms of its precision and utility, as an evolutionary hangover we have a preference for language with musical qualities.

Some """evidence""" for this claim:

- The most interesting fact is that gibbons sing similarly to humans, intentionally targeting a pure tone so other gibbons can harmonize in octaves. They seem to use this for bonding and communicating their vocal state. So there's precedent for musical communication in one of our closest relatives.

- Music seems useful for hominids: just like modern humans, our pre-language ancestors possibly used "work songs" as a way for large groups of foragers to ping their status. Prairie dogs do the same with their chattering - if one critter goes quiet, the rest quickly realize something is wrong. There is no evidence that human language evolved after human music, but it seems more reasonable to me than the alternative.

- On the other hand, it's well-known that modern humans can be easily misled by speakers who use intellectual affectations to spritz up nonsense, and in general we tend to make lazy judgments about speakers and accept/deny their arguments accordingly. So, assuming this quirk didn't evolve very recently, I could see how "uses language musically" has the same (dishonest) social signal of intelligence as "uses big words all fancy-like," simply because 400,000 years ago the most musically talented hominids commanded the most social authority (even maybe when they shouldn't).