If either family has no history of certain illnesses, then I would say no. It is like buying flood insurance when you live on top of a hill. Things can happen but the probability is small. My understanding is that these chord blood storage banks are just used for your child in case of cancer, immune disorders, etc. and are not used for research. I could be wrong about that part.
BTW, I am a father of one and one on the way in March.