I skimmed the paper, and it seems to be saying something different.

Basically, there are often different ways of putting a particular idea into words. Sometimes the longer way might be clearer, and the shorter way might be more confusing. If you care about being understood, sometimes you will use the wordy option. This is what humans usually do.

However, LLMs have context windows. All else being equal, verbosity eats up more context. If the LLM is trained (with reinforcement learning) to reason most effectively, it can do that by using terse phrasing. Especially on certain tasks that really need a large context window. Why? Because being terse is like getting a larger context window for free.

But in another sense, it's not really free. You're trading off clarity for context window. Sometimes you have to choose between verbose+clear and terse+unclear. If you're biased toward terse, that will also shift you toward unclear.

I do agree that LLMs are verbose sometimes, though. I think they are also trained to please the user, and they see sharing extra knowledge and insights as a way to do that. I don't think this idea is in conflict with what the paper says. If an LLM's training rewards both spitting out neat bonus info and doing reasoning that requires making the most of its limited context window, then that LLM may generate a large quantity of text which is written in a slightly terse and confusing style.