If you think bias and indoctrination are something that only developed "over the last several decades," you're mistaken. This has been the case of all universities, since time immemorial. And the swing to the left started in the Sixties (at least in the US).
You are, of course, absolutely correct. I said the last few decades because that is, again, as you said, the current "phase" we are on.
We want universities to be places where ideas from a range of schools of thought mix and are able to be explored openly and without negative repercussions. I don't want the extreme right to own university thought any more than the extreme left. We know the consequences of mono-cultural group think are never positive. The canonical example of what happens when the extreme right owns university culture being Nazis, of course.
My personal view on this is that private universities can do as they please. Any university that is publicly funded, either directly or indirectly (government guaranteed loans are an example of this) must have faculty and a culture that reflects the nation with balance and openness.
The fact that our universities have tilted so far to the left isn't good for the nation. Anyone who disagrees with this should consider what things would be like if the opposite were true. If the right owned though at our universities it would be just as much of a nightmare in the making.
This interview with Niall Ferguson (Oxford/Cambridge/Harvard/Stanford professor) was a real eye opener. Some might disagree, but I think the topic warrants some thought.
Hey, careful with that "Nazis" label. It implies a lot of things that are a poor fit for politics in the USA. It certainly doesn't just match up with the extreme right.
Consider these examples:
FDR actually put one ethnicity, the Japanese, in concentration camps. Harvard (proven in court) and others are discriminating against people of Asian ancestry. In 2019, 44% of colleges had segregated graduation, with black-only ceremonies. The typical Planned Parenthood is in a black community, and the founder specifically wanted to prevent that community from making more people.
Are those people and institutions the extreme right?