Yeah, I definitely think they should limit undergrad programs. It seems like there are two (relatively simple) options:
1- Restrict acceptances to the CD major when high school students apply to the university. If they specify "CD" as their major, the school will only accept, say, the top 30 applicants. The other "qualified" people still attend the university, but must choose another major.
2- Require undergrads to take a year of prereqs (A&P, stats, physics, English, pre-calc, psych), then have them apply to the CD program. This is how the nursing program works at my school, and it seems to be an effective system.