@marlowe1 - up thread, you emphasized the cultural dimension for middle class students eschewing Chicago. Coming back to the financial point, though: you need to remember that, a middle class kid accepted to Chicago is almost certainly in the top 5% of applicants for all but the most tippy-top public schools.
So, to use the Penn State example, the middle class cross-admit between Chicago and Penn State will almost certainly be accepted into Penn State’s Schreyer Honors College. This student will have tuition, room and board all covered, AND will have access to the honors dorms, specialized research opportunities, classes, etc.
At Chicago, this student would be a run-of-the-mill admit, and would be looking at around 20k/yr in expenses (plus any travel costs, if they’re not local).
For a middle class family, the Penn State offer is highly appealing indeed. Also, these honors colleges do a wonderful job, and invest a lot of resources into their honors students (to the extent where, for a family with financial concerns, investing ~$90k in Chicago - for all its long term benefits - may not be better than taking another, great option with Schreyer).
And, that’s what makes wooing the middle class kids even more difficult. The exceptional middle class kid considering Chicago has tremendous low-cost options available too. And, for a family that is more price-sensitive than the upper crust (and the lower income who pay next-to-nothing at Chicago), those other options move the needle.
Also, re “Princetonization” - I don’t think this is just happening at Chicago. The wealthy and the lower income are the two groups that will receive the most preferences in admissions, and the student bodies at top schools reflect that right now.