I would imagine this is because there is a 'comfortable' rate of information exchange in human conversation, and so each given language will be spoken at a pace that achieves this comfortable rate.
So it's not that the syllable rate coincidentally results in the same information rate, but the opposite - the syllable rate adjusts to match the desired information rate.
I'd add it's probably also that 90%+ of conversation isn't about "data transfer" in the technical sense, but relationship building. So information volume isn't usually crucial.
Now let's see this work done in technical fields, especially change management, maintenance, emergency services, etc, where time is crucial. Those environments tend to have very "coded" language, so we don't have to say a paragraph whenever we call for a very specific function/tool/action.
I suspect the languages would still have similar curves, but the data rates would increase.
I believe the percentage for information exchange is a bit higher, even in everyday life. I mean we also socialize, talk about the weather etc. But many times I open my mouth, I actually want to convey some information or gather some... That probably varies widely between cultures (and individual people and rhe exact social setting). I read some people like to chat with their cashiers while others don't. And for relationship building we also have body language etc so lots of that doesn't even need verbal language.