Use of large language models might affect our cognitive skills

It already is. College kids today are mostly skipping their essays and just editing AI created one. Their literacy seems somewhat low, although that could be bias (the lower ones might be the ones seeking out AI).

These sorts of effects are common. As animals are domesticated, their intelligence goes down. If you don't have to think for yourself, then your skill and its utility goes down. If you don't need to hunt for your food, then you don't need to spend energy thinking about it, and you become lazy.

I'm convinced this is happening in at least some humans as well.