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It's a two-way street. When someone tells you "don't do that", they usually mean they don't want to be on the receiving end of what often amounts to LLM-powered literary diarrhea.
Yes, in theory, the quality can be the same or better than human output. In practice, the tool creates two problems: it's too easy to produce walls of text for no compelling reason, placing asymmetric burden on the recipients; and it's too tempting to click "send" without reading because you're "90% sure" the email / doc is correct, wasting everyone's time multiple times every week when it isn't.
* do nearly as well
Anyone who believes the objective quality of the end result is the sole end goal of all tasks will have no self worth when technology surpasses them. This is true for essentially any task, because there is almost no end result that cannot be done "better" by technology.
However, the blog post explains that this is the wrong way to think about writing. The very first point made is that writing makes you understand your subject better and develop better ideas.
Characterizing the argument as 'thinking oneself to be Shakespeare' is a silly strawman and helps nobody.