MIT sounds like an outlier. Perhaps there is a unique explanation, such as asking accepted + matriculating students to submit scores over the summer before attending if they have them, like Bowdoin and various other colleges do.
A comparison of admit rate between test optional and test submitters at other selective private colleges for which I could find info below. The median of the 9 selective private colleges with information for the full class was ~50% of applicants test optional vs ~40% of admits test optional, which suggests test submitter admit rate was ~1.5x higher than test optional admit rate. For example, 15% admit rate for submitters vs 10% admit rate for non-submitters.
Test submitter applicants are expected to be stronger on average in the full application (expected to average higher GPA, higher course rigor, better LORs, better ECc/awards, more ALDC hooks, higher income, etc.); so I don’t think it is clear that the non-submitters were being significantly penalized for not having a score at typical selective, private colleges.
Total Class (ED/EA + RD)
Wellesley – 60% of applicants test optional, ~50% of admits test optional
Barnard – 59% of applicants test optional, 47% of admits test optional
Colgate – 59% of applicants test optional, 40% of admits test optional
Boston U – 58% of applicants test optional, 43% of admits test optional
Tufts – ~50% of applicants test optional, ~41% of admits test optional
Davidson – ~50% of applicants test optional, 36% of admits test optional
Emory – ~50% of applicants test optional, 31% of admits test optional
Amherst – 49% of applicants test optional, 37% of admits test optional
Vanderbilt – 44% of applicants test optional, 39% of admits test optional
Only ED / EA
Penn ED – 38% applicants test optional, 24% of admits test optional
Notre Dame REA – 49% of applicants test optional, 31% of admits test optional