Any sort of atrophy of anything is because you don't need the skill any more. If you need the skill, it won't atrophy. It doesn't matter if it's LLMs or calculators or what, atrophy is always a non-issue, provided the technology won't go away (you don't want to have forgotten how to forage for food if civilization collapses).
Right. But (1) no longer needing the skill of thinking seems not obviously a good thing, and (2) in scenarios where in fact there is no need for humans to think any more I would be seriously worried about doomy outcomes.
(Maybe no longer needing the skill of thinking would be fine! Maybe what happens then is that people who like thinking can go on thinking, and people who don't like thinking and were already pretty bad at it outsource their thinking to AI systems that do it better, and everything's OK. But don't you think it sounds like the sort of transformation where if someone described it and said "... what could possibly go wrong?" you would interpret that as sarcasm? It doesn't seem like the sort of future where we could confidently expect that it would all be fine.)
Getting worse at mental arithmetic because of having calculators didn't matter much because calculators are just unambiguously better at arithmetic than we are, and if you always have one handy (which these days you effectively do) then overall you're better at arithmetic than if you were better at doing it in your head but didn't have a calculator. (Though, actually, calculators aren't quite unambiguously better because it takes a little bit of extra time and effort to use one, and if you can't do easy arithmetic in your head then arguably you have lost something.)
If thinking-atrophy due to LLMs turns out to be OK in the same way as arithmetic-atrophy due to calculators has, it will be because LLMs are just unambiguously better at thinking than we are. That seems to me (a) to be a scenario in which those exotic doomy risks become much more salient and (b) like a bigger thing to be losing from our lives than arithmetic. Compare "we will have lost an important part of what it is to be human if we never do arithmetic any more" (absurd) with "we will have lost an important part of what it is to be human if we never think any more" (plausible, at least to me).
[1] I don't see how one can reasonably put less than 50% probability on AI getting to clearly-as-smart-as-humans-overall level in the next decade, or less than 10% probability on AI getting clearly-much-smarter-than-humans-overall soon after if it does, or less than 10% probability on having things much smarter than humans around not causing some sort of catastrophe, all of which means a minimum 0.5% chance of AI-induced catastrophe in the not-too-distant future. And those estimates look to me like they're on the low side.