Back in 2016, we had a wonderful exchange of views on the nature of profundity in the arts. The whole objectivist/subjectivist thang was aired as part of the discussion, as was the linked Understanding versus Appreciating a work. These topics have a life of their own, but I enjoyed this thread very much and trust that others might also. Just my opinion. But just try the first page....
See 4chamberedklavier's post below for link to old thread.
It would be tough to define in a comprehensive way what is meant by "profound" in the case of a work of art. (I would argue it is impossible, but let's pass over that rabbit hole.) However, I would go so far as to suggest that art that successfully conveys profound ideas is far more likely to survive the era, the social and cultural context and the specific factual circumstances in which it was created. The word "classical", especially when applied to art, traditionally referred to the culture of ancient Greece and Rome. It still generally refers to art of an earlier period or era.
If we gauge the profundity of art by looking at the impact or influence it has had over an extended period, well past the era in which it was created, we are using an ex post, empirical approach, famously advocated by David Hume in his 1757 essay, On The Standard Of Taste.
This empirical approach, often called the "subjective" approach here at TC (a rather misleading term, in my very humble opinion), while far from the only possible approach, has considerable advantages. Not surprisingly, in the 260+ years since Hume's essay, empiricism has had a successful run in aesthetic and many other fields.