Yeah a lot of schools went to this model years ago - I'm not a big fan per se especially with declining enrollments all around. Typically the President reports to the Board and is responsible for administration (technically the Principal reports to them). Still this is a good change for Rice
The old model worked when priests, brothers and nuns were a dime a dozen...literally.
Now, schools must pay a predominantly lay faculty and staff a living wage. Tuition doesn't cover it all. Schools need to upgrade their facilities, and tuition covers none of that. Fundraising has become critical to the life of a private school.
You can't have one person take the point for both academics and operations/mission advancement. That is trying to fit the old model into the new reality. It would result in one person doing too many things in a mediocre way, and too few things well.
Someone needs to take the point on mission advancement that includes fundraising, marketing, and recruitment. Be the face of the school. That's the President. He or she needs to ensure the financial stability of the school and carry out the school's strategic direction. He or she needs to hire a Principal to stay on top of the academic side of the operation and keep it strong.