Liberal arts disciplines such as this one train students in thinking and communicating.
Such graduates are likely to be adaptable, innovative, and effective leaders.
It may be more difficult to get one's foot in the door with this kind of major, but the employer that gives those grads a chance will profit thereby.
Too many graduates of pre-professional programs are trained to be nothing more than replaceable drones.
A traditional liberal arts education, focused on the classics (including one classical language), a modicum of mathematics and hard science, history, literature (as both were taught before the 'post-modernists set in) and at least one modern language requires solid work and gives one precise the sort of intellectual preparation for adaptable, innovative and effective leadership. Especially if combined with solid experience in team sports and social dynamics.
Much of what passes for a 'liberal arts' degree now (which includes all of the social sciences, all of the 'ethnic and gender' studies, communications, etc.) is just nonsense and fits one only to become a parasite.
I agree with your points, both the value of the education and that it's difficult to get in the door.