So if I was looking at enrollment purely on the basis of number of student bodies vs. net revenue generated by those bodies, and the school was in deep financial trouble, I'd be thinking of cutting nursing first. And then there would be no need for the lone physicist (or the lone biologist) to teach science requirements for the nursing students.
Students show up because they dearly want to be nurses or pre-med or whatever. Not having those programs, regardless of whether any particular individual will be successful in acquiring the degree, means those students simply don't come to your institution. That's bad, because that means you have little shot at the students who are moderately prepared and have at least some direction.
Yes, nursing is a hugely expensive program to run and we tend to be just about at the break-even point due to the required caps, but it's not because of the one chemistry class and one biology class we make those students take. Physics is not required for nursing.
However, our psychology, social work, art, and a particular language majors would be hurting for students if we didn't have large numbers of aspiring nurses who come, realize nursing is not their path after floundering the first year, and then change majors.
We have a couple majors on campus that benefit greatly from pre-meds who don't make it through the second year, including psychology again.
I've done the calculations on what students declare and where they go after they change majors. Almost no one changes into nursing, education, or pre-med, but many students remain at our school after taking a shot at those majors and then realizing how much they love psychology or really wanted to help people by going into social work. In fact, psychology does almost no recruiting in high schools because they pick up so many students after taking the required psych intro classes for a major that doesn't pan out.
What's hurting us most right now is having no engineering, the most popular major group among high ACT scoring students. Our coaches are hugely frustrated at losing good recruits year after year who know exactly what they want as a major and we don't have it. Instead, we get the students who really don't care about their major, but are choosing college mostly on where they will get the most playing time on the field. We would be in even worse shape if we had no pre-med, pre-PT, or nursing to offer people who think they know what they want as they chose primarily based on athletics or proximity to home (a big nursing draw).