Unlike product XYZ*, there was a time in very recent history when these same schools ran successfully with much smaller administrations. At some point you have to ask - do you want to save the cancer, or the patient?
*I am humoring your hypothetical, but there are in fact many cases where a small team outperforms bloated, ossified companies, e.g. the Britten V1000 motorcycle, or the recent article about wedding planning software (https://news.ycombinator.com/item?id=43133174), or the older article on the windows terminal (https://news.ycombinator.com/item?id=27725133)