There are MBA’s in every sector of business, not just banking, but technical and industrial areas. This is not just the US. You are speaking from a very limited and uninformed perspective,. I have a cousin that studied engineering went into technical sales then got an MBA and began to run a business unit in a semiconductor company. He went to Princeton so he could have gone to banking with just the undergrad degree but he didn’t want that lifestyle. Meanwhile he is extremely successful running a company that puts up satellites and has never worked as an engineer excepting a summer internship. His engineering degree game him the background to manage engineering projects and departments.
As far as entering graduate programs, whether or not you are required to have an undergraduate degree in a related area is very specific to the type of graduate degree you are seeking as well as the specific grad school. There are computer science MS that do require a degree in CS or at least math, engineering and some universities will require you to take some prerequisites if you do not have that CS degree. There are other universities that offer a degree for non-majors and they build the prerequisites in. But for astronomy, physics, and research degrees you usually are competing with people who had significant coursework and research in the area. In archeology, undergraduate degrees are rarely offered. But to be admissible you would be expected to have some training in classics, history, art–you might already be expected to know some ancient and modern languages.
Wacky courses are an undergraduate thing. Sometimes colleges have interesting or offbeat classes that will satisfy general education (or lower division undergraduate requirements) or distribution requirements. I once took a class called ‘Crime and the Arts’ which was about art crimes that occurred throughout history such as destroying national treasures in war, stolen artifacts, purloined paintings, forgery, and came all the way op to modern times to discuss graffiti, media and other ethical issues. This satisfied some of my breath requirements outside of my major and was one of the most enjoyable and interesting classes I’ve ever had and it covered history, art, ethics. You will not find general classes like that in grad school. Grad school is advanced work after foundations from undergrad in writing and general knowledge are satisfied. Grad school is focused in one area and even often a very specific sub-area such as a World Region for archeology or in computer science Artificial Intelligence or Theory or Security. You are expected to already have done preparation for your major in your upper division coursework. Some areas you can do post graduate studies to prepare.
MBA, you don’t really need anything other than work experience if you can get a decent program to accept you. In MBA prestige can matter quite a bit. Many other schools it does not. For science and research degrees, the overall reputation of the graduate school is something entirely unrelated to the undergraduate prestige and selectivity. NYU has programs they are very good at for grad school and others that are unremarkable compared to a school your parents never heard of. That isn’t how people pick grad programs here. University of North Dakota, for instance has a Space Studies program that people from all over the US and the world attend. NYU would not compare.
Oh, and there aren’t too many jobs for people with MS in astronomy or archeology either.