It is not ridiculous to hope a student goes to a school that likely has better classes available in the fields that matter- math along with computer science. The strengths in other fields are meaningless. btw- Notre Dame does not rank that highly compared to many schools in other STEM fields. Many people erroneously think that being private and competitive means being better than public options. Flagship U’s serve two populations- the ordinary better than average college student (the average go to other state schools) and the high end students who take the honors courses and may not be able to afford the private schools (plus the fact that there is not enough room for all who can excel in them).
Get over the prestige factor for school name. Be sure to look at individual majors and opportunities for the student. People from the coasts often forget that there are some great public institutions in the middle of the country (some are above Ohio State, btw).