Unfortunatly that seems to happen quit often. But many young students forget to think wether CS is really the subject they want to study.
That's very true. If I would have had better knowledge of the exact contents of the CS studies, I don't think I would have started them. It's hard to know how things will turn out when choosing studies or more ahead, jobs. Hindsight is always 20/20, but I would have better started something else. You are right about the "what would I like to study if there was no CS?" Probably nothing scientific at all, I don't like numbers. I like to be creative, more to the artistic side, quite the opposite of scientifical studies and especially CS, it seems...
So, to return a bit to topic and not bore y'all to death, yes, I think there should be basic math in CS degrees, but in proportion to what is useful to the average graduate. The point that they might have to write seriously mathematical software is rather invalid, in my personal opinion. Why don't you require medical/legal/linguistic/... knowledge too, then?
It would be better to provide specialization options in each specific type of study, e.g. math degree with a cs option, med degree with cs option, etc. This will be more useful since computers are used in about every profession these days, and CS majors can't be expected to understand all of these fields just because they might have to program for it. By using people who studied something more relevant to the type of specialized software being written, the specific needs and problems will be easier to capture, analyze and solve.