This is a cynical view of what students want. I think you're underestimating the influence that professors have over young developing minds. There is an intellectual war being waged on university campuses, and students are being used as cannon fodder.
Postmodern Marxists have virtually taken over humanities, and have been extending their reach outward through the soft sciences for some time now. I would argue that this is directly related to the lack of critical thinking skills developed in universities.
Postmodernists view logic and rational thought as tools of oppression used by white males to subjugate women and minority groups in Western cultures. This became a convenient philosophy for Marxists who could no longer rationally defend communism after its repeated failures in the early 20th century. And this is the philosophy being pumped into the minds of students.
Hence, you see students of these far left academics violently shutting down free speech across university campuses. They have nothing to gain from rational debate. Their feelings and subjective interpretations trump any form of reason or critical thinking.
Jordan Peterson would argue that what young people really want (and what would be good for them) is responsibility. Because responsibility gives an individual a sense of purpose and moral agency. And currently, these values are mainly being cultivated by the right side of the political spectrum, which is why I think you see younger generations shifting towards conservatism.