And it should come thus as little surprise that these skills – a sense of empathy, of epistemic humility, sound reasoning and effective communication – are the skills we generally look for in effective leaders. Because, fundamentally, the purpose of formal education in the humanities, since the classical period, was as training in leadership.
When I look at who gets nominated and selected for most leadership positions today, I see people chosen by other powerful people for the purpose of entrenching and extending their existing power. Part of the reason that US citizens have such trouble with science is that we have never had a culture of epistemic humility and rarely selected for that trait in our leadership. Looking up lists of "great leaders" turns up people like Adolf Hitler, Winston Churchill, Napoleon Bonaparte, Alexander the Great...many of whom possess the "effective communication" trait but fall quite short of "empathy and humility".
A fundamental difficulty of justifying the humanities is that the humanities cannot tell you how to think about the world. The best it can offer is a tour of how other people have thought about the world and a series of exercises which hopefully take you from imitating other ways of thinking towards developing your own. But the exact process of developing that perspective cannot be taught — indeed, that goal denies the student-teacher dichotomy and requires instructors to view students as junior junior faculty rather than as consumers of a product. This difficulty is not unique to the humanities; STEM fields face it as well:
There is no “The Scientific Method,” and science offers no path to truth. That may seem paradoxical at first, because science offers innumerable, excellent methods, and is the most reliable path to truth.
I'll stop short of trying to pick out why our society doesn't value this process, but I suspect that it's multi-faceted and I have no real idea on how to "sell" humanities-for-everyone to people with money and power.
(And, I mean, have you read modern humanities papers? There's certainly an argument to be made that "the humanities" are just as uninterested in selling humanities-for-everyone as most people are in buying it.)