Penn. Columbia. MIT. All of them have long ago planted that flag. The difference is in the execution.
One can now say that MIT has already reached number 3 since it’s perennially added as the M to HYPSM (Really, already number 1 globally in many peoples minds because it’s an 800 lb gorilla in the categories it dominates)
MIT proves that there are more than 3 schools in the “top 3”
To be “top 3” UChicago only has to be the top choice of a sizeable population of applicants. And be considered a consistent and respectable alternative to half of HYPSM so that even if overall it’s somewhere between 1 to 6 in peoples minds and in US news, it washes out to “top 3”.
UChicago is trying to do more with less $$$. As long as it continues to execute well it will continue to do so.