There are a lot of great points here. A couple more to consider:
With private banking, while you do pay the fees for storage, your baby's chances for a match to itself are 100%, and between 25%-75% for baby's immediate biological family ( mom, dad, sibling). And, you don't have the large fees associated with pulling out a "withdraw" as you do with public banking because you are already paying the small annual fee for storage.
People often think about the big diseases down the road, but don't forget about the more common things that can happen during the birthing process such as lack of oxygen that causes issues which are being resolved currently using baby's own stem cells.