I don’t have some overarching rationale or theory about whether an inteview is truly optional or not, but I’ll offer our experience in last year’s admission cycle for our very high-achieving (but not shy or awkward) math kid.
Wherever it was possible to turn down the opportunity to interview (e.g., Princeton), our kid did that, on the theory that an interview is a random component largely determined by some amorphous “fit” with an unknown interviewer. It is not worth much, and could have a downside.
For top schools, accepted at Princeton (opportunity to interview explicitly rejected in the app); Yale (no interview offered); and Amherst (opportunity to interview rejected in the app). Waitlisted at MIT (after accepting an interview offer), chose not to remain on the waitlist. Rejected at Harvard (affter accepting an interview offer).
There were other T20 acceptances and waitlists but those were the highly selective ones, and our kid did not interview anywhere else but Harvard and MIT. FWIW. My guess is it is ok to put down on the Princeton app that you don’t want to interview.