this study has a grand total sample size of 170 (that's 10 speakers per language), it also measures syllable rate (i.e. syllables/second times diversity of syllables) as a proxy for information. this is pretty far from how people will intuitively conceptualize "information".

i would take the results too seriously.

The belief that that these 170 speakers, each speaking many long passages in 17 languages would converge to 39bps through dumb luck is unlikely enough to be almost mystical.

edit: If I hear a case that is not insane as to how the numbers could somehow determine themselves (through bad math) or be p-hacked, I'd happily consider it. Instead people are acting like taking sentences of equivalent meaning and counting the syllables to determine information density is somehow laughably naïve.