Nonsense. Times New Roman was and is a beautiful accomplishment, and we are lucky that our society has widely standardized on such a beautiful font.
It captures the beauty of old style and transitional types like Garamond and Baskerville, without demanding the aristocratic luxury of space that these older fonts demanded, and without their stylistic pretensions. It's compact and has a high x-height. It's everyday; it doesn't connote literary snobbishness or state authority; it's the font of presses and shares its dignity with the everyday people who use it.
This excerpt's thesis seems to be that using a common font shows you don't care about your typography. This is true to some extent, but you can show you care while still making the excellent choice of Times by, e.g., using optical variants for titles, footnotes, and call numbers, and for God's sake turning on the fi ligature in Microsoft Word.
Mr. Butterick's fonts are also beautiful, but there's no need to shit on Times New Roman to sell them.
I find Times New Roman very easy to read and available on many platforms.