I'm going to play the devil's advocate here: couldn't you argue that whatever you did to win a Nobel prize is already (supposedly) a significant contribution to society, making additional contribution via taxes unnecessary (or, in fact, discouraging); as opposed to, say, winning the lottery.
There is already a tax rule just for those prices, that "picks winners and losers"; it would be a matter of removing conditions from that rule (that the prize must be donated), not adding another.
Sure, but why isn't, e.g., being a teacher not a significant contribution? Or, for the sake of this argument, being the founder of a wildly successful company that employs thousands of people? Look, I'm against taxes as much (and probably even more) than the next guy, but making exemptions for prizes is plain irrational.