But starving the overhead function -- the part of the operation concerned with establishing internal policies and procedures, risk management, evaluating past performance, board development, and all the other "back room" functions -- is setting your nonprofit up for long-term failure or serial crises (and then, often, failure).
Nonprofits are like farmers --- a good farmer doesn't just put in crops and harvest them. A good farmer leaves the soil in better condition than before, so that the same land can be used to produce crops year after year. Nonprofit programs --- the services delivered to the community --- are the crops. But if you just put all your energy into crop production, the soil is going to get short-changed. Over time, yield goes down or the inputs required to maintain the yield keeps going up. Here's a good article by one of the authors of the Oregon Nonprofit Corporation Handbook on this dilemma.