These are the same arguments that were advanced against tax-supported education down through history, "not everyone needs this much education", "it is too expensive to provide this education to everyone, we can't afford it", and "education is a personal good, not a social good, the individual should pay for it, not the society." (The last is my personal favorite.)
But like the people who argued against tax-supported education, they are wrong. The US gained a lot by educating everyone.
I would be willing to bet that at some point these people would have advanced the equally specious argument from the right that our current income inequality is due to the level of education required to be considered in the middle class in today's economy. If you don't think that these arguments contradict one another I would appreciate an explanation of your thinking.
Conservatives are right that a university education is elitist. It always has been. The universities cull through their students to try to find the very few who can advance the body of knowledge that we all depend on for real progress. They are trying to find the few each year who can do research, most of which won't produce anything meaningful, to enable that one eureka moment of the real advancement of the body of knowledge. The more people who are exposed to university education the better chance we have of progressing.
Conservatives are right that a university education is a liberal experience. But not in a political sense, in the way that foreign travel for most people makes them more tolerant of different people and cultures, exposure to different ideas and different ways of thinking makes most people tolerant of these things and less dependent on the ideas of the past and traditions that are the hallmarks of a modern movement conservative.
The costs of a university education haven't gone up because the administrative overhead of the universities, it has gone up mainly because of the lower support from the government for higher education, primarily to lower the tax burden on the wealthy, a goal of conservatives.
In my view, conservatives are letting their preferences for lower taxes on the already rich and directing all of the gains from growth in the economy to the already rich stand in the way of the progress that produces the growth. This will kill progress. It isn't the already rich who produce the growth, it is the people who work for them.
Forty years of feeding the rich have already reduced one component of growth in the economy to zero, productivity gains. The primary driver of productivity growth isn't automation, it is the education of the workers. It is starting to kill the other component of growth, innovation, as profits become too easy to make. Corporations no longer have to compete with innovation, they now increase profits by finding new sources of cheap labor, by paying their workers less.
Burdening students with the crushing student debt hurts our economy too. At a time when the college graduates should be buying a car, buying a house, having children they are doing none of these things because of their student debt. The reason that the so-called Reagan economic miracle happened wasn't the lower tax rates but because the baby boomers entered the workplace and started to earn money and to spend it, on cars, houses, started families, (and the growth in defense spending by deficit spending, i.e. increasing the national debt, Keynesian fiscal stimulus.)