Appropriateness aside, I think the real reason we don't have a Nobel for Biology is probably a result of the fact that Alfred Nobel cared more about the pursuit of knowledge for the betterment of the human condition, rather than for its own sake. I imagine he learned the limitations of the latter approach the hard way through personal experience considering his most (in)famous invention...
Physiology is a more descriptive term for this work. You could argue this is "cell biology", but that's just a claim that these fields are exclusive of each other; much modern physiological work is now understanding the underlying molecular processes (maybe it is molecular biology?).
His work on molecular mechanisms has brought better understanding of higher level processes in the body and traditional "physiologic" mechanisms.
I meant that the prize itself should be renamed to biology because physiology is-a biology and the prize often is awarded to things that are biology rather than medicine or physiology which are highly specific.