I think that "messages need to be coarse-grained and contain little nuance," as stated in the comment, is a comforting thought, but it has little truth to it. I just have observations, many of them anyway, and not any proper experimental or observation study, but reflecting on them has changed the lens through which I look at leadership and management.
When you say in the previous comment that "it's easy to assume that words are intellectual garbage, but that's not always the case," I see the position/authority bias at work: it can't be nonsense, they are the leaders, what they say has to make sense, if only seen in the context of having to speak all day, or to dozens, hundreds, thousands (unlikely outside of politics) of people every day.
Or look at the layoffs at Twitter, Meta, Google, etc.: even if they seem to make little sense (some of the decisions anyway) in the way they are done, somehow they have to make sense, either because the layoffs are a "blunt instrument," or because the shareholders are asking for something particular or whatever.
I would like to bring an example. A person in my company was hired in a management role, overseeing a function for a group of hundreds of people. As soon as they gave their first "speech," it was clear to my shrewd eyes that the words uttered made no sense, that they were lying about their past, their accomplishments, and that their skills were not what was advertised. If I focus my attention on what people do in a context where I am competent, it takes between very little and not much to assign them to a broad range of competence: incompetent, somewhat competent, okay competent, very competent.
Similarly, I've played a couple of sports at a high level, and if I see people training for, say, an hour, I can assign them to a level of competence, with little margin for error. The guy who does everything differently and originally is sort of an invention of novels and TV shows. Sometimes, very rarely, they show up in real life, so I might add a little bucket labeled "mysterious."
The executive hired by my company fell squarely into the category of incompetent. But because the executive had been hired into that management position by people deemed competent (they weren't, that's why it was a flywheel, a charade), my colleagues considered the executive competent for years, despite the obvious nonsense. It was rather bizarre to observe, but position bias (and "whatever" bias) is as strong as many of the biases related to physical characteristics that we carry around with us all day, every day. And when I tried to explain to my colleagues what I had seen, they did not believe me. I think they still don't believe me.