You have it backwards. Today, most universities engage in indoctrination of students to one degree or another, and virtually 100% of that indoctrination is geared to pushing the student Left politically.
As for the poorly educated and Fauci Plague, the stupid--who you are really talking about--often are hurt by their lack of intellect. You can have a PhD and still be stupid...
I think the COVID pandemic has been a real test of that line of rhetoric. What we had is a pretty simple exercise in common sense: would people get vaccinated and greatly lower their risk from the virus, or would they be swayed by conmen and propagandists and avoid the vaccine, resulting in much higher rates of serious illness and death?
If one thought of universities as places that debilitated people's reasoning abilities by way of political indoctrination, then maybe you'd predict that the people with advanced educations would make worse decisions about vaccination. Maybe, for instance, those "too educated for their own good" academic types would be talked into thinking vaccines can't be trusted because of "something something corporate big pharma," or other lefty drivel. And maybe those who hadn't been subject to university indoctrination would retain their common sense and take that simple step to protect themselves and their loved ones.
Of course, we now know that's not at all the way it worked out. Low education levels ended up being strongly correlated with vaccine hesitancy. The poorly educated were more likely to fall for anti-vax propaganda, and thus more likely to die during the pandemic.
It's interesting, too, because it's linear. It's not like you reach a certain level of education and after that you've got diminishing returns where common sense gets overwhelmed by academic mumbo jumbo. At every step up the ladder, people were more likely to make wise decisions about vaccines. High school graduates were more likely to be vaccinated than dropouts. People with some college were more likely than those who only graduated high school. College graduates were more likely than those who'd only had some college. Those with graduate educations were more likely than those only with undergraduate degrees. And those with MD's were even more likely than those with other graduate degrees. It's pretty much a straight-line correlation.
So, the pandemic really destroyed that talking point about advanced education being bad for people's thinking skills. It turns out that when it was literally a matter of life-and-death, the more education you got, the more likely you were to take the wiser course of action, driving down your own risk of death and that of your loved ones.