Earlier quoted context omitted.
It’s not only their core strength — it’s what transformers were designed to do and, arguably, it’s all they can do. Any other supposed ability to reason or even retain knowledge (rather than simply regurgitate text without ‘understanding’ its intended meaning) is just a side effect of this superhuman ability.
I see your point, but I think there's more to it. It's kind of like saying "all humans can do is perceive and produce sound, any other ability is just a side-effect". We might be focusing too much on their mechanism for "perception" and overlooking other capabilities they've developed.
However, I do think that in this case it's meaningful. The claim isn't that LLMs are genuinely exhibiting reasoning ability — I think it's quite clear to anyone who probes them for long enough that they're not. I was fooled initially too, but you soon come to realise it's a clever trick (albeit not one contrived by any of the human designers themselves). The claim is usually some pseudo-philosophical claim that the very definition of reasoning is simply 'outputting (at least some of the time) correct sentences' and so there's no more to be said. But this is just silly. It's quite obvious that being able to manipulate language and effectively have access to a vast (fuzzily encoded) database of knowledge will mean you can output true and pertinent statements a lot of the time. But this doesn't require reasoning at all.
Note that I'm not claiming that LLMs exhibit reasoning and other abilities 'as a side effect' of language manipulation ability — I'm claiming there's no reason to believe they have these abilities at all based on the available evidence. Humans are just very easily convinced by beings that seem to speak our language and are overly inclined to attribute all sorts of desires, internal thought processes and whatever else for which there are no evidence.