I assume talking about the USMLE since the NBME offers other tests that med students take during their clinical years that are generally referred to as NBMEs,
The short answer is–no, there is no public data set that shows the USMLE pass rates and average scores of all US medical schools.
BTW, you do understand that USMLE scores are more reflective of an individual student’s effort & test taking ability than it is of a med school’s curriculum. There is substantial data the shows a significant correlation between MCAT scores and USMLE scores. Simply put: students with high MCAT scores tend to score higher on the Step 1 than students with lower MCAT scores. (Corollary–schools with high average admitted MCATs tend to have higher Step 1 scores than schools with lower average admitted MCAT scores.)
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5045966/
General USMLE test results are available here:
https://www.usmle.org/performance-data/
More data about USMLE scores here:
https://www.aamc.org/initiatives/cir/406438/10a.html
https://www.fsmb.org/siteassets/usmle-step3/pdfs/2017-annual-report-on-usmle-to-medical-licensing-authorities.pdf)
The LCME sets minimum pass rates for US allopathic medical schools as part of their accreditation standards.
http://lcme.org/publications/
Schools that are underperforming (less than ~93-95% first time pass rate) will find themselves on probation and their accreditation in jeopardy.
USNews Graduate Compass (subscription required) purports to report the STEP 1 scores for every US medical school, but there's no way to verify the accuracy of the numbers they report.