It depends on what metric you rank colleges. For example, if you are ranking by endowment per student, which is a key driver for most other rankings including USNWR and perhaps the ranking that has been most consistently correlated with the acronym, then the order would be:
1 . Princeton – $2.8M
2. Yale – $1.9M
3. Stanford – $1.6M
4. Harvard – $1.6M
5. MIT – $1.5M
…
49. Columbia – $0.4M
However, perhaps the most important reason is that HYPSMC is already used… typically in a reference to C for Caltech, although the C in HYPSMC could also be a reference to Chicago or Columbia. It’s completely arbitrary. You can type "HYPSMC "in forum posts if you like, but don’t assume everyone reading the posts will know you mean C for Columbia.