Earlier this decade, a computer simulation showed that, because of the Dunning–Kruger effect, a democracy cannot consistently elect better than mediocre people:
Mato Nagel, a sociologist in Germany, recently implemented Dunning and Kruger's theories by computer-simulating a democratic election. In his mathematical model of the election, he assumed that voters' own leadership skills were distributed on a bell curve — some were really good leaders, some, really bad, but most were mediocre — and that each voter was incapable of recognizing the leadership skills of a political candidate as being better than his or her own. When such an election was simulated, candidates whose leadership skills were only slightly better than average always won.
I'm not sure if anyone has tried to research this further. However, it comes to mind that if this result is true, it can be extended to academic fields of study.

Education is commonly divided into STEM – science, technology, engineering, math – and liberal arts. This division roughly follows the principle that fields in STEM have an objective test of truth; while liberal arts don't.

In fields with an objective test of truth, popularity is important, but results passing objective tests is more important. In fields without an objective test of truth, only popularity of the results (and their authors) is important.

If the above is true for democracy – if the Dunning–Kruger effect means mediocre politicians get elected – then the same should be true for fields of study that lack an objective test of truth. Somewhat like democracy, such fields become a popularity contest. Because of the Dunning–Kruger effect, what's most successful in this contest will be mediocre.

The result is that not only are the elites in these fields going to be mediocre, but the entire field is going to be filled with mediocrity. This is in the same way as if you turn on CNN or MSNBC or Fox News, it's going to be pointless nonsense.

Furthermore, this is not news; we understand this intuitively. In STEM, the term "liberal arts" is almost an insult, a repository for the lesser able. In turn, those in liberal arts accuse people in STEM of smugness, arrogance, and superiority. Of being out of touch.

The Dunning–Kruger effect, I think, explains both.