Why would the school having less students than the interest can cover be a problem?

Not many investors would assume a long term return of 10% over inflation. If they target 7% instead, it would almost exactly fund that enrolment level.

You're assuming there was no need-based tuition program already running. Average tuition may not be full tuition.

10% interest seems like a stretch in today’s environment. 5% interest from US Treasuries would be a more reasonable baseline: yielding $50,000,000 per year total, or $40,000 per year for each of the 1,250 students.

Based on https://www.treasurydirect.gov/auctions/announcements-data-r... the "safest" seems to be an assumption you should use TIPS, and you get about 2.2%

Can you do better than that? Almost certainly! But at least TIPS has some inflation protection built-in.

Assuming 10% interest is not realistic. The inflation-adjusted rate of return of the S&P 500 is 6.8%. Plus, the inflation rate of what it costs to train doctors has gone up at a much higher rate than the overall consumer price index.