Matthew Phelan, Journalist, former Chemical Engineer, proud Houseplant Owner of three
This is a valid concern and a genuine possibility—as dystopian as that might seem.
For example, Time magazine recently reported on a policy in Japan that encouraged universities in that country to "focus on disciplines that 'better meet society’s needs,'" meaning exactly this kind of shift toward more technical, applied science, and math training and other "skilled trade" varieties of education. The policy didn't meet with anything like total compliance or acquiescence, however. The president of Shiga University, Takamitsu Sawa, called the proposal “outrageous” and the government ministers proposing it “anti-intellectuals” in her op-ed for the Japan Times.
An important consideration here in America, is that liberal arts and humanities departments are feeling a pincer-like pressure from two sides: it's not simply politicians who are seemingly opposed to funding liberal arts and humanities education, but students themselves are flocking to the more technical degrees. (There's a New York Times article from 2013 about this issue of student interest at Stanford, and the problem it has posed for their liberal arts and social sciences programs.)
I think, arguably, this trend against a well-rounded liberal arts education is pretty poisonous to the basic tenets of democracy and its requirement of having an informed populace, and it's hard to imagine fine arts, liberal arts, humanities, or social science departments disappearing overnight. It's impossible to predict the future, but I think it's inarguable that we'll be making this decision collectively as a society with the officials we elect to state and federal office, with our personal choices of college majors, with our weight as alumni donors, as activists, and the like.
Speaking as someone who double majored in Chemical Engineering and History as an undergrad, I can't recommend enough pursuing some kind of high-contrast dual degree track. I minored in English also, and I frequently noticed that the students pursuing just a liberal arts degree treated the reading as drudgery, whereas to me it felt like a nice break from some mentally taxing calculus problems. And, alternately, the math and science work would occasionally feel like fun Tetris-style puzzle-solving when I was tired of critically reading some complex rhetorical argument about medieval agrarian society (or whatever).
Ultimately, what I am saying, is that this is a credible threat and that it's up to us, by our individual choices and actions, to defend and maintain the intellectual and cultural traditions that the liberal arts, social sciences and humanities represent.
I hope this was helpful.