I know there is an ongoing debate about the worth of a liberal arts education in the modern economy, but there's something to be said about the traditional notion of education for education's sake, rather than as a mechanism to improve lifetime earnings.
Something should be done about the high cost of post-secondary education and the untenable burden it places on many students, but I disagree that the solution should be tied to job prospects.
If you take away the student loan subsidies then the cost of those liberal art programs will inevitably come down, or at least they will be restricted to just the people that can afford a house worth of tuition to study philosophy.
I'm not seeing any direct correlation between the cost of an education program and the earning power of graduates from the program, so in the absence of that evidence, I couldn't say with any confidence that tying subsidies to earning power will do much at all to bring program costs down.
If I were to guess, what's more likely to happen is these programs would be canceled wholesale at low-margin institutions, leading to an effect opposite that which you describe: liberal arts programs would be available only at the institutions where graduates are more likely to obtain well-paying jobs, meaning Ivy League and other prestigious (and expensive) institutions.
Simply limiting access to federal loans across the board, rather than subsidizing STEM/MBA degrees at the expense of liberal arts, would probably do much more to incentivize the reduction of post-secondary education costs without completely ditching the notion of a liberal education.
Where this rule would pinch would be high cost institution that nonetheless produce graduates that enter low paying jobs.
Taking your premise that society has an interest in an educated populace, and that includes people studying liberal arts at the tertiary level, does it have an interest in paying for the most expensive providers of that education?
What benefit does society get from having lots of graduates with $100 to $200k in student loans that they'll struggle to make payments on for the next 20 years? Education is perfectly fine, but if the goal is to encourage lots of people to study liberal arts for the sake of learning, then let's find a way to do that that doesn't cost $50k per year.
If society has an interest in an educated populace, then we should go ahead and make college free for everyone by funding it directly with taxpayer money, versus indirectly with student loans.
In Canada, the degrees with high earning potential (HBA, CS, Engineering) cost 2-3x more than the other programs.
It's really quite aggravating because they charge you based on your declared program, even if all the courses you're taking are actually arts courses.
Producing well-rounded citizens is very important for a functioning society, therefore, it makes lots of sense to create incentives to produce well-roundedness.
Taking Calc III and a fourth science class is a lot less valuable to me both as a worker and as a citizen than any one of my economics courses. (To say nothing of my public speaking courses.)
That's what most people go to university for. That's how universities (at least around here) advertise themselves.