It is usually large public schools that are relatively high in admission selectivity that have this issue with CS (and engineering majors), since they have large numbers of students who are interested and academically capable of doing the CS major.
Less selective public schools are less likely to have this problem, since many of the students find CS too hard to want to major in it. Small colleges (public or private) are less likely to have this problem if they have a decent number of CS faculty, since the number of potential CS majors is limited by the overall college size.
But check each college individually before applying to avoid unpleasant surprised after enrolling.