Before I write anything regarding the topic of CrossFit for Sport Performance, you need to know that I am 100% pro-CrossFit. I have no major issues with the methodology or thought process behind that style of training, and in fact enjoyed the benefits I got from doing that style of training for several years before I decided to chase some strength goals of my own.
In the Strength and Conditioning world, it seems that whenever someone mentions CrossFit, everyone is all on board or acts like CrossFit killed their mom. It can be a polarizing thing. Coaches have very differing opinions on it, and when it comes to sport performance, some are all for it and others are still want it to die off (which I don't think will ever happen).
So why or why not use the same methodology that now crowns the Fittest on Earth every year to train an athlete to compete in sport? First, you need to understand the purpose of CrossFit, its definition, the purpose of the CrossFit Games, and then also understand the purpose of sport performance training.
CrossFit's aim (per their website) is to increase health and fitness; to "increase work capacity across broad time and modal domains"(crossfit.com). I think the following paragraph from their website is a great summary:
"Overall, the aim of CrossFit is to forge a broad, general and inclusive fitness supported by measurable, observable and repeatable results. The program prepares trainees for any physical contingency—not only for the unknown but for the unknowable, too. Our specialty is not specializing." -CrossFit.com
In the same statement of what CrossFit is (found here), they end by saying that "The needs of Olympic athletes and our grandparents differ by degree, not kind." This is where the difference between CrossFit and sport performance lies.
Sport performance, and the field of strength and conditioning, aims to improve performance in a specific sport. This comes in the form of creating strength in the necessary plains of motion, musculature, and ranges of motion specific to the athletes' sport. While CrossFit aims to create balance, sport performance - in some manner- aims to create a planned imbalance. Training an athlete to perform at the highest level in their respective sport requires planning a specific outline to create the specific traits needed for the sport.
This is where the concept divides people on the subject. While there is no doubt that CrossFit is creating the fittest people Earth, that does not mean they are creating the greatest athletes. Although the elite CrossFit athletes in the world are by all means highly athletic, they would probably not be a standout in a single sport.
However, I do believe that there are some instances when using CrossFit for sport performance can be a good thing for a few various sports. I think the same for training athletes solely as weightlifters has the potential to bring about great benefits. At some point in the span of a year, most athlete's have a period where the focus is to build GPP (General Physical Preparedness). This is where (depending on sport and coaching), a period of training CrossFit could be beneficial for athletes. Depending on sport, the period may be shorter than others, or it may be longer than others.
There are a few sports, in my opinion that could benefit from the utilization of CrossFit in their training program in a longer format. These sports tend to be the combat sports (wrestling and Jiu Jitsu primarily), as a wider spectrum of fitness is needed to adapt to the varying style of match that can take place. However, the vast majority of sports would not benefit as much to train in that manner for a long duration of time due to the sport specific or positional needs of the athletes playing them.
Overall, should CrossFit be used for sport performance? I think the answer is "It depends." It depends on the phase of training and the demands of the sport. It depends on whether or not the athlete in question is a multi sport athlete (this is more relevant for high school athletes). It also depends on whose coaching and programming, as that can also be an important factor. You see, whether or not you should utilize CrossFit for training athletes isn't as a clear a line as some make it out to be, so in the end the answer will remain "It Depends."