I strongly disagree agree with the classics having any cultural relevance outside of the elite class. It entirely dismisses the bulk of all media commonly enjoyed by people in the period, which has more significance to society and its politics. Focusing on the classics filters everything through the point of view of the people in power, which is an incredibly poor way of understanding the world.
Besides the classics were elite fashion. Like speaking French or fencing. They were a means to distinguish class, with hard to access knowledge and habits. It wasn't because these things were good, it was because the average person could not easily attain access to them.
The great books canon was partly constructed retroactively by people with agendas about what civilization meant. A real collection of classics would have much more folk stories, common herioc figures and fantasies.