>or is people's ambivalence towards elite universities 100% irrational?

    am·biv·a·lence  /amˈbiv(ə)ləns/ noun
    the state of having mixed feelings or contradictory ideas about something or someone.

>A lot of Americans support these attacks on universities. Why do people harbour this much animosity towards these institutions?

There are a lot of very real things that are rotten in academia if you exclude the social politics center to this article.

So when people see they're loosing federal funding... yeah, some will think along the lines of "eh, whatever, fuck 'em, maybe they'll figure out how to clean their own house." Especially if the university is also known for both sitting on a large endowment and for prioritizing self-serving administrators over doing academics.