Taxpayers do this already: it's called grade school and high school. The public has an interest in an educated populace.
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.