I also think a lot of the appeal of many of the “top” colleges is being able to change your mind about your major, or indeed not really know your mind at the time you are applying.
So, while this is pure speculation, I would not be surprised if a decent number of people who end up with a Yale College Engineering degree either did not intend that when applying, or only had it on a list of possibilities.
I think this helps explain why the “top” non-tech colleges tend to make sure they are at least pretty good in everything they offer. Among other reasons, they want to make sure people can decide on, or change among, all their majors while at that college.