Given the sheer volume of email she sent from her blackberry (lunch meetings, when to get up, where to go, can you print this, happy birthday, etc) it's pretty clear it's her primary way of communication. So that explains her refusing to take no for an answer from the NSA.
If her motivation was to block FOIA requests, then why did she do literally all important and confidential communication on paper, which falls under FOIA? Then why did the entire administration accept her use of a private email server if she didn't have an obvious reason why she needed one? If her real motivation was to dodge FOIA, then why was the NSA stonewalling? The FOIA hypothesis raises far more questions than it answers.