Web dev is big. It deserves to be a major. You could probably have a 4 year specialization on various parts of web development. And you'd be highly capable and inextricably linked to those specializations for years after graduation. And it all may change from your Freshman courses to your Senior courses. Op was suggesting that situation is limiting. You could substitute "robotics" for web dev, by the way, and it would still stand.
Coming from a small midwest school as you did, your coursework should (and does) skew towards current-skill-based specializations which help you get a job. This is OK and desirable for the vast majority of students.
By the way, I also went to a small midwest school, and its "Computer Science" program was cancelled in favor of more skill-based specializations (right after I graduated with a CS degree). I don't blame them, but I stuck to my theory / fundamentals because that's what I wanted.