In general, I do think that wrist wraps are overused. That said, I have had a wrist injury myself and I do use them. The following are just a few quick notes on wrist wraps for weightlifting and gymnastics movements in CrossFit.
Warm up without them: You don’t need wrist support until a large load is coming through the joint. Some coaches would even say you don’t need them until you are at a max lift. The wrist is designed to move into the extension (cocked back) position required to hold a barbell, a handstand, a push up position, etc. The wrist is also designed to be able to withstand compressive loads (as in a handstand). If you have an injury or the weight is heavy, by all means, use the support. But, in general, wait until the load is getting heavy to use them so that you do not become reliant on the support. Consider that if you are relying on a lot of gear or accessories to support your weightlifting or gymnastics, you might need to take a look at your technique and see where you could benefit from stabilizing the movement or getting stronger.
Don’t tie them too tight: wraps should be snug but not cutting off circulation. You can consider using a thicker Velcro-bound powerlifting-style wrap which provides more support for those heavier weights overhead if you really want to block motion. The alternative is a cotton wrap that is thinner and more flexible for lighter weights or when you need the wrist to be a bit more free in its motion ability.
Don’t place them OVER the wrist joint: while you do not want the wrap to be too far onto the forearm (providing no support) and you do want to prevent excessive wrist extension, remember that in many movements you are wearing the wraps for, you need to actually extend the wrist. That is to say, if the wrap is covering the joint line, you might be causing dysfunctional movement to happen at the wrist when you go into wrist extension positions, say, as in a handstand. Be mindful of the movement you are going to perform and if you are in fact blocking that movement. Again, the wrist is designed to do this and if you block the motion at the wrist, you WILL get it somewhere else. Our bodies are good compensators and though this is a great feature of evolution, it can certainly lead to musculoskeletal injury.
Don’t ignore the actual problem if the wrist is just the victim. The biggest culprit of wrist pain is poor thoracic, scapular, and shoulder mobility leading to an ineffective rack position (more on this position here). Consequently, the wrist then becomes injured as the athlete compensates and gains too much mobility from this downstream joint rather than looking up the chain at the problem area. In these cases, stretching the wrist is not only unproductive, but can be injurious as the wrist is likely already overstretched.
I also see a lack of wrist control when holding a barbell over head. Make sure you are gripping the bar correctly and maintaining a neutral wrist as much as possible with overhead lifts. Consulting with a coach or physical therapist on this can be useful.
Wrist wraps are certainly an inexpensive and useful tool for CrossFit and weightlifting athletes. Just be sure you are an educated user so that you can get the most out of your training and avoid injury!!