The expected utility of giving blood is currently very small, at least in the USA, because people are not being refused transfusions due to lack of blood. If that started happening blood drives would expand hugely and you'd know about it.

I have heard statistics (from sources that aren't the red cross) that the supply of blood in the US is nearly always quite low. Running out rarely happens, although I did hear that lack of adequate blood reserves did cause a problem on 9/11. My impression is that the Red Cross typically has enough reserves for a few average days, but if something major happens, that supply can get used up pretty quickly.