@Cue7 I don’t get exactly what you mean by Penn not having varied “types” of students. I see where you are coming from in that Students tend to get very involved with many on campus groups, such as clubs, societies, and sports, but I do not know if this purports into a “lack of diversity”, especially compared with other schools with high achieving students who also juggle a lot of things in their life. There is this feeling at Penn that your peers are doing and achieving so much and you need to stay on pace, but again I don’t think this is too different from many other top tier schools.
First off, they were already admitted to their specific undergraduate school because their intended pursuits align with the specific goals of the school and careers they are going for. Aside from the combined-double degree programs (yet another example of Penn caterizing to specialized future pursuits), The students in Nursing (only undergrad program in the entire ivy league) were admitted because they showed in their application that they were very focused and passionate about pursuing nursing. Same with Wharton and business/leadership. Again, you can say that about other top tier schools too.
Moreover, I know many students who do a lot of activities, but it is focused and aligned with their professional goals. Penn is very pre-professional and for example, you will see a good chunk of Wharton students who do LOTS of activites, but they are all business-related (investment, consulting, finance, management etc. club, wharton-[insert country] society/exchange, Case competitions). You may find the same with Pre-med students (Pre-health frat, some medical club, volunteering work, working in a lab).