cognitively speaking
That's not what the damn study says.
People who wrote an essay with an LLM did not show signs of having having written it themselves, on account of, they hadn't. Just like I couldn't tell you the remainder of a long division I put in a calculator, because it went straight to a mantissa. I didn't lose the ability to to math. (At worst, I don't wanna, now that I have a calculator.)
The only long-term aspect of this study was a dozen people coming back months later and switching sides. So even pretending it's asking the right questions, the tabloid interpretation should expect to see the brain-only essayists fumble it and the LLM essayists sharper than ever. But that's plainly not what happened.
They didn't even measure essay quality. It was just about EEG activity, incidental recall, and self-reported degree of ownership. But that nerd shit doesn't get clicks, so every fucking headline is like Does chatbot is brain damage?! or Permanent cyber-psychosis ten minutes!! or If men learn this, it will implant forgetfulness in their souls. They will cease to exercise memory, calling things to remembrance no longer from within themselves, but by means of external marks. It is no true wisdom that you offer your disciples, but only the semblance of wisdom, for by telling them of many things without teaching them you will make them seem to know much while for the most part they know nothing. And as men filled not with wisdom but with the conceit of wisdom they will be a burden to their fellows.
Oh sorry, that last one was Plato arguing against the detrimental cognitive effect of books.