Well, the students could withdraw from the school - walk out protest.
Parents could demand return of tuitions which they saved up for so many years so their kids could receive a "liberal education". Nothing more irking than Alumni pressure.
Unrelenting public ridicule is the best medicine for Churchill's "problem" and the problem of Churchill.
The problem is that if he has few students, so much the better for him -- less grading and his own little band of devoted disciples.