Pragmatically, for a prospective student, it's a giant pain simply because it's hard to tell what a program bearing one of these names will actually teach you! Some "computational biology" programs will include wet-lab work, others will never let you near a pipette. Some bioengineering programs are almost purely physical-machines engineering; others use the word interchangeably with "bioinformatics." And so on.
But somewhere in that mess is the future of biology, medicine, and probably some other things as well.
I imagine it'd be pretty easy to do that today given the state of math edjumacation in American schools (never went to one). Looks like the bulk of it is calculus and not even the rigorous kind or the kind that could at least be immediately applied to problems today. A 1368 pages calculus book doesn't have a word about something as immediately useful as Gamma function (comes up a lot in today's compsci). Wouldn't it be more fruitful to chop all the current calculus sequences and instead have a semester of finite-dimensional vector spaces first followed up by a semester of functional analysis while introducing only the important bits of analysis as one goes? The relevant bits of mulitvariable calculus and differential geometry of curves and surfaces could be easily introduced within the framework of linear algebra within the first or second semester. That way students could progress to the frontiers of math and bleeding edge of engineering and sciences much faster. As it stands right now, it seems to me the students are forced to waster time, energy, money, potential on memorizing how to solve old chestnuts like the optimization problems from the single variable calculus that were (probably) barely relevant in the middle of the last century.
-- Alexandre Grothendieck, "The Life of a Mathematician - Reflections and Bearing Witness" (1986)