Apparently, umbilical cord blood is much quicker to get to the patient who needs it than stem cells from bone marrow. The umbilical cord blood is already sitting in a facility, whereas bone marrow would require scheduling a surgery from the donor. (The umbilical cord blood is used in many cases where bone marrow transplants are traditionally used.) A medical courier can get the blood from one side of the country to the other very quickly (within 12 hours I would say). I think that in most cases, people who would need the blood don't need it so urgently (like in the case of organ donation). Rather, I think it is mostly cases of people with cancer or other disorders that are not quite as time-sensitive.
Thank you for the education on this matter. I had no idea.