But the point of Olympic medals is to assess skill. If the available pool of talented athletes is larger than the number of gold medals, then there is a need for more gold medals.
Different fields have different balance between these two things.
http://induecourse.ca/the-bottleneck-in-u-s-higher-education...
"That kind of school" is (call it) a Top 10 school in a given field. And there is always going to be a shortage of slots at Top 10 schools whether you have 1,000 schools or 10,000. What potentially makes sense is investments in relevant subject areas in schools that aren't in the Top 10 but are in the Top 100 so they're functionally less distinguishable--except in prestige perhaps--though arguably that's already the case. In the US, cost aside, a qualified applicant can already get into a "good" school.
For schools, like Harvard and Yale, isn't a large part of the value they provide to students derived from the school's network of alumnus and the prestige the school's name holds? If so, don't these schools derive a large part of the value they offer from their exclusivity?