I am not sure whether it would make more sense to just retire the abbreviation.
For undergrad there are hundreds of excellent colleges and universities. I think that students focus far too much on the highest ranked universities.
For graduate school the list of the top schools is going to depend upon your major. As one example I have a daughter starting a DVM program in September. The top five universities in the US for DVM programs (#1 through #5 in the country for veterinary medicine) have overall USNWR rankings of #39, #18, #153, #80, and #53. The top schools for what was my major (Math) would be completely different schools. Nothing is in the top 5 for both majors and whether anything is in the top 10 for both will depend upon which ranking you look at (Cornell and Wisconsin probably being the closest).
However, I do agree that Columbia is a very good university. If we did add a C some might take it to mean Caltech, and some might feel it is ambiguous regarding whether it stands for Caltech, Chicago, Columbia, or something else (perhaps Cornell?). Perhaps the ambiguity might be a good thing.