My school (UVA, in the late-90s) already had recently converted Computer Science as a limited enrollment major to get around this problem. Declared CS majors had preference for CS courses. It wasn't quite so bad that others were completely locked out, but if you weren't declared, you had to be quick to register and might not always get into fun electives (the core courses were usually larger and easier to find a seat).
Since that time, they've actually added a second CS major. They now offer the original BS in CS through the engineering school. And a BA in CS through the college of arts and science. The two primary differences being a foreign language requirement for the BA students, and a heavier emphasis on math and general engineering in the BS program.