The main issue I see is that the methodology section of the paper limited the full time to 20 minutes. Is this a study of using LLMs to write an essay for you, or using LLMs to help you write an essay? To be fair, LLMs can't be swapped between the two modes, so the distinction is left up to the user in how they engage in.

Thinking about it myself, and looking at the questions and time limits, I'm not sure how I would be able to navigate that distinction given only 20 minutes. The way I would use an LLM to aid me in writing an essay on the topic wouldn't fit within the time limit, so even with an LLM, I would likely stick to brain only except in a few specific case that might occur (forgetting how to spell a word or forgetting a name for a concept).

So this study likely is applicable to similar timed instances, like letting use LLMs on a test, but that's one I would have already seen as extremely problematic for learning to begin with (granted, still worth while to find evidence to back even the 'obvious' conclusions).