My son showed no interest - he didn’t visit and his first choice had been MIT. I think he was probably better off at CMU.
Would your S be happy at Penn State even if he doesn’t get into the honors program? If not, he needs some other likely admits. Everything else on his list is reachy, if for no other reason than those schools have low acceptance rates. If he likes math, look at UMD-College Park. Great department, easy to double major in CS, lots of brilliant kids. Count me as a +1 for looking at Case and Pitt. If he likes data, look at applied math programs.
Am the parent of S who got a math degree along with lots of grad CS courses; most of the schools on your list were ones my S considered seriously. He went to UChicago. S was on the math team but did not do much in the way of the big math competitions – he was seriously involved in the CS equivalents and research that got him some big awards. He majored in math to enhance his CS tool kit and to prepare for a PhD in theoretical comp sci. He’s at a SV company doing lots of big-picture language and algorithmic development, which he finds more fun than research.
My DH was a decision sciences and accounting major at Wharton. It was lots of playing around with data, and he learned lots of useful skills that he applies every day in a non-math, non-CS job.
So keep in mind that to apply to Dietrich students don’t need to declare majors until sophomore year. Perhaps he can write an essay linking two fields – e.g. computer science and decision science, corpora analysis and linguistics, computational learning and Cognitive Science, that would fit to together in a coherent essay. I would stay away from asserting he wants to study Stats – as I mentioned it is the “hot” major this year and they are anticipating an overabundance of students going into this concentration.