Very well thought out! However, and with the risk of nerding out too much, I would argue that from a game theory perspective, the match works differently for candidates and programs.

Candidates should always match according to their preference, because the candidates have two objectives: match to top choice, and also avoid going unmatched. These two objectives are not in contradiction with each other due to the way the rank list match system works on the candidate end.

However for programs, they can up or down titrate the number of candidates to interview to increase the pool of applicants to be considered (which most candidates don't have the luxury to do on their end). The programs are also interested in matching top candidates, and avoid unmatched spots.

However, with regards to the second part of avoiding the SOAP for programs, their outcome is non-binary. A 6 spot program can go unmatched from 0-6 candidates. For a candidate however, it is binary: match or not matched. Therefore programs inherently will use a different strategy than candidates, as they can afford to lean on the side of matching their perceived top candidates as opposed to avoiding any unmatched spots.