Should society pay more toward the education of students who?

Given time, the market should sort this out without government tinkering.

The problem is that the government is already fouling up market signals by making student loans so easy to obtain that they look like "free money" (for a while).

If students had to pay the full cost of worthless Majors, they would stop attending.

Likewise, so long as students see that STEM grads get far better salaries, then they will move to stem Majors.

They are now. At the graduate and doctoral level most STEM students can get GAs and research grants to pay for their entire schooling. While students in the humanities and fields where there are few jobs get little if any funding for advanced degrees.

The undergrad level is used to sort out the best from the average students.

My daughter got a 3/4 ride for her masters and is on a full ride for her PhD in engineering. However, at that level the US has a shortage of qualified instructors as many of them are offered more money to go into industry.

In Australia a system like this is already in place most australian students are under commonwealth sponsored places, meaning the bulk of our fees are paid by the government and the rest we pay afer we reach an income threshold.

A percentage the government pays is dependant on the demand for grads in that area, meaning they government pays a greater precentage for students who study science and maths compared to students who study Law and Business.