Those classes are what make college different from trade school. You may think it sounds like a meaningless platitude now when you just want hurry up and be done with the whole thing, but many of those "extraneous" classes will make you a more rounded person if you allow them to.
I'm a vastly different person at 33 than I was at 18, I'm interested in different things now partly because I was exposed to subjects I wasn't particularly interested in at the time. 15 years later, I'm glad that my past self sat through art history, biology, and economics.
In my family, myself and my brother have been successful by focusing on one or two skills and honing them. That was made much harder by the education system, which fought us the whole way, because it sees specialisation as some sort of problem when it is in fact the solution. In my brother's case the school tried to insist he went to university. He didn't, as he knew full well what he wanted to do and reckoned, correctly, he would do better without being a student. In my case the university insisted that I take non-CS classes despite that I was paying them for a CS course. The classes were interesting, but marked arbitrarily (i.e. one essay at the end and who knows how it's evaluated?). I nearly got kicked out of CS because of a single essay written on archaeology!
As I go through life, I constantly encounter people who thought they were "learning how to learn" or "learning how to think" when they went to university, only to discover after graduation that they had no particular skills and were seem as essentially worthless by the job market. It's tremendously depressing for them and creates constant, lifelong insecurity.
Critical thinking abilities are something you want on top but are not a substitute for actual, hard skills. And they are certainly not something a university can teach - please. All the stats and studies show that universities are incredibly ideologically homogenous and rapidly stamp out any political thought that deviates from their left wing consensus. Universities teach people that thinking and disagreement are dangerous, that opinions are "triggering", and speaking out loud leads to exclusion. They're the last place on earth I'd expect critical thinking skills to emerge unscathed.
Critical thinking skills aren't something to have on top of domain-specific skills, they're something to have as a foundation for them. If you focus on critical thinking skills in lieu of anything domain specific, and expect to get a job without further learning, you're foolish, but you'll have an easier time learning the specific skills you need for practical work anyway.
The humanities have a long tradition of debate and disagreement as a path to seeking the truth, that is sometimes lacking in sociology or political science.
The OP said that they only wanted to take classes directly relevant to their future career. Biology and economics are examples of classes that I didn't think were relevant to my career (at the time).
>But as for art history - how much would you pay for such an education, specifically?
The first time I went to college I had a full ride scholarship, so I didn't pay a dime. The second time I paid, and I took another art history class. I think I paid about $1500 total for that course.