The Problem with Universities

I have had the following conversation a number of times recently:

1. I want to do X. X is a lot of fun and is really interesting. Doing X involves a little of A and a little of B.
2. We should get some students to do X also.
3. Okay, but from where should we get the students? Students in Department of A don’t know B. Students from Department of B don’t know A.
4. Fine, maybe we could start a program that specifically trains people in X. In this program we’ll teach them A and B. It’ll be the first program of it’s kind! Woohoo!
5. Sure that’s great, but because there aren’t any other departments of X, the graduates of our program now have to get jobs in departments of A or B. Those departments complain that students from Department of X only know a little of A (or B).
6. Grrr. Go away.

Has anyone figured out a solution to this problem? Specifically, how do you train students to do something for which there’s no formal department/program without jeopardizing their career prospects?