For example

But SMU is not a serious candidate for anything. Like Rice University, it's too small and too private.

I'll agree with you that SMU isn't a serious candidate. But that's not explicitly a result of being a small private school.

Wonder how I know? Here's a list of enrollment at a few private schools:

Notre Dame 12809
SMU 12373
TCU 11379
Wake Forest 8495

Clearly none of those could ever be considered P5 schools right? All are small private schools after all...

And just because I believe in bringing receipts:
SMU enrollment -> https://www.smu.edu/Provost/IR/Statistics/FactSheets/Fall2020Facts/StudentEnrollment2020
TCU enrollment -> https://www.tcu.edu/news/2020/tcu-total-enrollment-up-3.2-percent.php
Wake Forest enrollment -> https://bulletin.wfu.edu/enrollment/
Notre Dame enrollment -> https://www.nd.edu/about/