Point of interest on this subject; While attending classes with instructors from NFCC (National Fastpitch Coaches College) there were sessions with differing views on throwing techniques. I'm old school and many college coaches in other courses were very conscientious about proper throwing form, pleading for us to teach the basics to players to insure less chance of injury. While taking a course that included fielding techniques the great Bill Edwards and Jay Miller pointed out the need for infielders to be able to accurately throw sidearm as a method to save time. Certain situations require the need to become "creative" to get an out. Speed kills in this game and the older girls can get down the baselines pretty quick when they want. Edwards would have the girls practice fielding a ball barehanded and throw to a target. They would charge a ball lying stationary on the ground and flip the ball barehanded to a base. They had timed the girls to show the difference between that and setting and throwing to the base. It was quicker. However; I never saw/heard them say a catcher should do it.
Keep in mind these coaches were/are working with some of the greatest female athletes that play our game. The expectations are very high. The players are extremely well conditioned. They have the field smarts to know when they need to get "creative" and when to save their body. As mentioned, the sidearm motion normally affects the elbow while any joint including the wrist can be strained by unnatural motion. A true "sidearm" throw normally will add extra torque to the elbow. I say this because there is a difference between "throwing sidearm" and bending over and throwing with proper form. While watching the coaches work with the college players, it was obvious to me that many were indeed throwing more over the top but with the torso at a more parallel to the ground position rather than being perpendicular. The time being saved was from them not straightening up. This throw would add more strain to the lower back area but would mitigate any elbow or shoulder strain.
What I believe many coaches miss when instructing the art of throwing while working with a catcher is the fact that many "lean" over partially to get some added torque from the shoulder muscle and chest area, not that uncommon of an outfielder trying to throw hard from the fence to home plate. The body will naturally have more strength in the motion this way because there is less resistance in that motion, thus allowing the muscles to pull thru 'cleaner'. I believe many misdiagnose a throw as "sidearm" when it may truly not be the case. The demonstration being held by Miller and Edwards, I saw maybe 2-3 sidearm throws. The rest were power throws from a bent position, they simply did not step to the target due to their momentum carrying them in a different direction. They threw across their body.
Proper throwing form provides the least chance of injury while getting the most power in a throw. We aren't always granted the luxury of setting up a throw. The closer your position is to home plate, the quicker you need to react to a play. In my opinion, a catcher should never throw sidearm at any time. She'd be better off throwing underhand than throwing sidearm if it meant responding to make a play. We never need to worry about those natural athletes with good technique. It's the athletes with poor throwing habits, normally developed in the early stages of life, we need to constantly instruct. Just be sure what you are teaching. Girls react to instruction if you detail the reasoning "why" they need a good form and need a clean throwing technique. They still need to know that it's their call to get creative to make a play.