I've got nothing against students who don't know what they want to major in, as I started in psych/anth/soc and ended up switching to business when I realized I was going to need to be able to get a job when I graduated.
But my "general management" non-specialized business degree didn't do me much good when most of the recruiters were looking for accounting majors for Arthur Anderson and the like. So I took a test, got picked up by the Feds, and ER'd 29 years later.
I have had some sort of small side business (largely hobby but it has turned a decent profit a few years) much of the time since I got out of school, so that is where the smattering of business study has been most useful.
But my school expenses didn't qualify as a major financial outlay, and $40K a year sounds pretty significant to me if the student is basically just cruising around pretty much aimlessly. Aimless cruising can be had for a lot less than that!
As was pointed out the only thing you need from the prestigious university for most employers is going to be the university name on your diploma, and that doesn't necessarily require a full 4/5/6 years to be spent at that one place.
It sounds, from what I hear about nieces going to college, that if you are a decent student there is often a pretty decent amount of financial aid that can be had from the small (but not hugely prestigious name) colleges, as they don't have as many people trying to get it, and they often may have a decent endowment that allows more help to the students.
But in the Feds there certainly seemed a pretty wide array of degree fields (and the occasional MA/PhD/JD advanced degree) represented among my coworkers. I'm sure that if you are working as an engineer in an engineering firm, you'll see a lot of people with engineering degrees around you. But for general industry/retail/government/small business stuff some sort of degree just seems to be an easy thing to ask for to thin the herd of applicants, and the degree field or comparitive prestige of the institution doesn't seem to have much impact.
I encourage the students in the family (the siblings, not ours) to take at least some basic business courses as electives as I think that like taking shop AND home ec classes everyone needs that kind of basic knowledge.
Oddly enough, they don't often seem to take that free advice.
cheers,
Michael