No, but it does mean that little girls no longer learn to write greeting cards to their grandmothers in beautiful feminine handwriting. It's important to note that I was part of Generation X and, due to innate clumsiness (and being left-handed), I didn't have pretty handwriting even before computers became the norm. But I was berated a lot for that, and computers supposedly made everything worse. It was a bit of a moral panic.
But I admit that this is not comparable to chatbots.
LOL - you might not want to believe that, but there is nothing to cut down. I actively steer clear of LLMs because I find them repulsive (being so confidently wrong almost all the time).
Nevertheless, there will probably be some people who claim that thanks to LLMs we no longer need the skills for language processing, working memory, or creative writing, because LLMs can do all of this much better than humans (just like calculators can calculate a square root faster). I think that's bullshit, because LLMs just aren't capable of doing any of these things in a meaningful way.