To be honest, reading that essay reminded me why I (personally) don’t enjoy classics more than modern work: the language of modern works is already familiar, making for a far more enjoyable experience.
I do enjoy some classics (love Dostoyevsky), but in general if I open a book and find the prose to be more of a hike than a stream, I don’t open it again.
It doesn't take inordinately much practice/exposure to get into the flow of (good) past writing in a language you are fluent in, and if you keep at it, it gets easier with practice.
You do have to pay a bit of attention to words whose meanings have drifted over time; comparable to false cognates in a foreign language.
Keep in mind many classics are translated and retranslated in a contemporary tongue. I was reading some Plutarch and found it incredibly accessible and easy to read - most Latin texts that I have read are quiet easy.
Until I started reading them I was expecting something more like the Bible - so terse it is exhausting.
Which is not, again, a reason not to try.