With regard to almost all undergraduate courses, you will not “use” the subject matter of the course later in life. The purpose of these courses is not to transfer knowledge to you, as in so many facts or even so many tools, because all of that in available for free or nearly so, from the internet or in old-fashioned books. With a few exceptions (e.g., accounting, nursing, engineering, elementary school teacher), the purpose of an undergraduate education is for you to develop your ability to think for yourself. Hence, “liberal education,” as in being a free person, able to decide for yourself.
As for what an undergraduate course in statistics should involve, it should enable you to deal with the mass of data that comes like a flood from the real world. To discern tendencies from oddities, to deal with phenomena having multiple causes, and with relationships in which both X and Y are causes and effects of each other.
The reason you have to solve some problems in a statistics course is not so you can save money not having to buy a computer. It’s to demonstrate you have grasped the material being covered. It could be that you really understand the meanings of central tendency and dispersion; but, if you are unable to demonstrate that understanding, I don’t know what an educational institution can attest to your understanding. Ideally, in a program of study, you (a) learn to master the standard tools of analysis of particular disciplines, (b) learn to apply those tools of analysis to relatively simple real-world situations, and (c) learn to integrate knowledge from multiple disciplines in relatively complex real-world situations.
I am sorry that you had an asshole for an instructor. Many colleges and universities are headed by people from the humanities who themselves are oblivious to complex phenomena such as we who are in social sciences, medicine, business and other such disciplines deal with. These administrators think statistics can be reduced to so many formulae, and can be taught by foreign graduate students who have difficulty speaking English, when all “gen ed” courses should be taught by faculty who have deep knowledge of their discipline.
Some smattering of Statistics knowledge certainly helps in understanding that CAGW is unprovable BS that is widely spread.