I am not sure what the purpose of having a $1.2 Billion endowment is if you are running the school budget exactly like ones that have an endowment that is less than 1/2 this. What are they doing with all this money? Faculty salaries should be higher and tuition should be significantly lower compared to these schools. In addition to free tuition, Exeter (and probably Andover) could afford to give students a $10,000 stipend for travel, books, computers, and clothing. The amount of money given by alumni (who benefited from this generosity and were grateful for the opportunity) would be more than the tuition revenue in the long run.
In all seriousness, there must be some point at which tuition contributes so little to the operating budget, that perhaps the only purpose for charging it is to provide an incentive for students to value their education.