Agree with the others. I also wanted to add that, IME, most students don't have excess credits by the time they graduate--they've often taken just enough to meet the minimum requirements for graduating. The programs are set up that way, so that they can be completed in a "normal" eight semesters (four years) or whatever. A lot of people would feel that taking extra courses, where they don't even need the hours but are done "just because," would be a waste of time, money, and effort.
All that is to say that by the time a student graduates, they don't usually have much wiggle room to decide which classes will go towards their degree--they've (hopefully) hit their minimum in every requirement but without room to spare. So even if an institution allowed a student to look back and strike something from their transcript (which US places usually don't, IME), most students wouldn't be able to do that anyway, because retroactively dropping any course would likely knock out some requirement for graduation (of hours, or a specific type of course).
Building a four-year schedule these days almost requires an engineering degree itself, it seems. There's the total number of hours you have to hit; often within that, a certain number of hours must be classes in your major or college. Your major will have specific courses that are required, and then lists like "choose 1 course from this list" and "choose 2 courses from this list." Some of those may have prerequisites (courses you have to take first), so you have to keep an eye on that. I took placements tests in English and math before starting university, and was required to take certain English and math courses based on the results of those tests. Also my university required foreign language experience, but having four years in high school counted for me; otherwise I would've had to take a couple years of university-level foreign language.
Then you have "general education" (gen ed) requirements meant to give students exposure to a broad range of topics no matter their major. As a science major I also had to take courses that counted as writing-intensive, a course in Western culture, a course in non-Western culture... History majors have to take one or two science classes. I'm interested in a broad range of topics and was fortunate to be able to study a lot of different things outside my major, from world religions to Viking sagas to music history to architecture. But, a lot of people hate the gen ed courses because they're not interested in those things, or scheduling has tightened up such that they have to take whatever classes fit in their schedule, rather than something they're interested in.