This is wrong, LLM are trained to mimic human writing not to mimic human capabilities. Writing is just the end result not the inner workings of a human, most of what we do happens before we write it down.

You could argue you think that writing captures everything about humans, but that is another belief you have to add to your takes. So first that LLM are explicitly designed to mimic human writing, and then that human writing captures human capabilities in a fully general sense.