I was actually surprised to see the level of controversy surrounding it.
Back in the day, when I was a college Student at Georgia Tech, I was granted the great privilege by the Athletic Director to use the athletic teams' weight room. This was when bars and bumper plates in a weight room were unheard of. It was also because I was weightlifting even back then and was on various National Junior Teams for weightlifting.
Anyhow, I always saw the baseball players doing Olympic lifts (very early 2000's, GT's team was very good). The only lifts which the athletic coaches shied away from were snatches, because they were worried about the pitcher's hurting their elbows. I remember seeing them doing cleans ( I think one of the athletic coaches of the GT baseball actually wrote a book on how he trained his athletes).
Now, many years later, having another great privilege of working alongside some of the best weightlifting coaches in the world, I think the question should be approached differently.
Athletic sports performance coaches should ask : what is the goal of doing the olympic lifts, and which lifts should my athletes do?
So, a weightlifters goal is to snatch and clean and jerk as much as possible.
A baseball players goal of lifting would be to become more powerful and explosive, and a small secondary effect of balanced use of both sides of the body.
Thus, baseball players do not need to train like olympic weightlifters. The best exercise would be hang power cleans- yes, not even full clean and jerks. There is a benefit to doing overhead work like the jerk, which is the most explosive part of the olympic lifts, in terms of acceleration. They might not need to snatch.
It seemed most of the controversy was over whether the clean put too much stress on the elbow and UCL. I have torn my UCL -- the answer is for a healthy elbow, NO.
Most lifters tear their UCL for two reasons - 1. bad technique in the snatch, 2. saving a lift that is going backward in the snatch at a near maximal weight (what I did ;).
To get the most bang for your buck in the olympic lifts is simple:
1. Teach the baseball players relatively good technique. If they can hit a tiny ball traveling over 70mph, I am sure they can learn how to do a decent clean.
1a. For example, The system I use, I can get someone to do a decent clean in 1 training session--especially, if they are already an athlete.
1b. Any exercise the athlete is doing requires technique. I have seen people mess-up something as simple as an incline bench. We should avoid the excuse that olympic lifts "are too hard to teach". Again, your players are highly athletic individuals, they can learn a good clean.
2. Reward consistently good technique. Technique should actually get better the more tired the athlete is - because it forces them to be more efficient. If their technique is starting to breakdown, then have them go down in weight-- you can even have them work with the bar for 30min.
3. Avoid singles and doubles, work in lower intensity zones-. If the goal is to get more explosive and not to be the best weightlifter, then doing lower intensity for sets of no less than triples is fine. There is no reason to do singles and doubles.
So, to answer the question, most elbow injuries do not happen in the clean. The clean is a very safe exercise when done with reasonably good technique. If anything, the clean will improve hypertrophy of the front delts, biceps, and forearms. The elbow is one of the few joints which can actually be better stabilized by increasing muscle mass around it. Doing cleans on a healthy elbow with good technique at reasonable intensity and reasonable repetition range/set may actually get the muscles, ligaments, and tendons in the elbow thicker, and , hence, better prepared for sport.
That's my humble opinion.
PS: And, I clean on my fully recovered UCL all the time ;).
*I think I saw the original topic, headline of this article, on a sports performance forum I randomly came across. Sorry for missing the citation. Content in this post is my own.