White probably wants playing time (plus the opportunity to play deep into the NCAA tournament). Barring injury, she won't start over Turner in 2017-2018. And, seeing Boley play, I think she will be a starter (over Westbeld) by her Sophomore year, when White would be eligible. Turner has the "5" on locked that year, and Boley/Westbeld will likely split time at the 4. Also consider that ND likes to often go small, especially since they have great guards/wings. I could see ND playing something like Patberg, Ogunbowale, Mabrey, Young and Turner for an extended amount of playing time (and if they land Walker....)
White would likely start in 2018-2019 though, but thats only 1 season. Not many people transfer to another school for reduced playing time.