Jeff pointed me towards an article in the New York Times which cites biomechanical studies apparently that the curveball isn't as dangerous for young arms as conventional wisdom would have us believe. Money quote:
Each study concluded that curves are less stressful than fastballs and, based on the data collected, contributed little, if at all, to throwing injuries in youth players.
So are common sense and years of experience totally off base here? Should young pitchers have the gloves taken off and start throwing curves willy-nilly? I, for one, am unconvinced that this is really meaningful. I can't speak for how physical development affects a mechanical analysis, so let's be more general about this.
In the sort of test the article references, 'stress' generally means 'elbow torquing' (I shall assume that this has not changed. If it has, please ignore). Two things immediately fall out of this. First up: Since the force imparted to the baseball is angular, a higher velocity out of the hand will therefore correlate pretty well to an increase in elbow torque. The force has to come from somewhere, after all. This makes the discovery that the curveball delivery is 'less stressful' than the fastball no discovery at all - it's essentially trivial.
Second, measuring torque in a joint is not the same thing as measuring ligament stress. It's a pretty weak oversimplification that does not accurately portray what goes on inside the elbow. The images below show ligaments compared to a torque diagram:
I could probably have rotated the diagram to make it line up with the elbow picture but I'm lazy. Anyway, the elbow is much messier than the cleanness of representing stress in torque form would indicate. The forces are somehow distributed throughout the ligaments in various directions, and it isn't even uniform because the soft tissues of the joint have different stiffnesses. The stresses we care about are in the ligaments rather than in the joints as a whole, which this sort of analysis misses (we can't yet do the sort that would be able to properly derive ligament stresses).
Throwing a curveball badly, as young pitchers are wont to do, doesn't add more torque to the elbow, but it will cause a twist in the arm, setting up a whole different set of stresses in the elbow (especially because ligaments are non-isotropic, meaning that they have different failure strengths in different directions). It could very well be that this causes the injuries that are apparently frequently observed in kids throwing the curveball*. The article essentially states that thrown properly, breaking stuff shouldn't really be any more detrimental than throwing fastballs, but we knew that already. Throwing while tired will also lead away from the 'ideal' curveball motion, as is probably a big factor in the warnings given by coaches against throwing too many curves.
As always, we should be moving away from the idea that we can accurately look at what motions cause/do not cause damage and towards what we actually know, and what we know is this: Pitching tired is much more likely to lead to injury than pitching fresh. So let's worry about not overusing pitchers rather than fret about what it is they're doing otherwise. Someday, we'll be able to look at stresses in ligaments and get a good idea on which motions are detrimental and beneficial, but attempting to do so now without all the tools in place is short-sighted. Playing things safe and letting their bodies say what's working and what isn't is probably better than just giving a blanket green/red light to pitches and deliveries.
*Do not take this as a statement of fact. It's not even a very strong statement of opinion.