Low-weight high-rep exercises, like they do in Crossfit, will do very little to develop "power" (which I'm assuming you mean to refer to being able to apply a large amount of force across a distance in a very short amount of time, i.e: explosiveness).
Power comes from fast-twitch type 2b muscle fibers, and the amount you have varies based on your genetic makeup [2]. Its possible to recruit the other types of muscle fibers to become fast-twitch type 2b but that requires continuous retraining of fibers through plyometrics; as soon as you stop your body will regress to its natural ratio of muscle fiber types. Fast twitch type 2b muscle fiber tires extremely quickly (I remember reading ~10s but I can't find a source) and is not something that can be trained using high-rep exercises [1].
Doing hang-cleans (never do these [3]), sloppy squats, "chin-ups" and other Crossfit staples for time in rapid succession and in high volume will only really help you lose weight and slip a disc in your back, but it will do very little to develop "power". If you want real power and explosiveness train like an Olympic sprinter: high-weight low-rep complex exercises and low-rep plyometrics [1].
Sources:
[1] http://smscsqlx.sasktelwebhosting.com/services/exphys/wts%26...
[2]
Arabatzi, F, and K Eleftherios. “Olympic weightlifting training causes different knee muscle-coactivation adaptations compared with traditional weight training.” Journal of Strength and Conditioning Research. 26.8 (2012): 2192-2201.
[3]
http://www.poliquingroup.com/ArticlesMultimedia/Articles/Art...