If you play a particular sport requiring fast movement, you should attempt to move quickly when practicing the particular sporting skills, thus demonstrating power, but not when exercising to build power.
Better Results.
If you consider the reasoning above, fast movement is not superior to slower movement in producing quick muscles, power or explosion. Moreover, the faster you move, the greater the acceleration and momentum. That means a quick blast out of the starting gates resulting in high forces at the commencement of movement. What follows (if not injury) is muscular unloading for part of the range of motion as the resistance propels upward and until gravity slows the weight down. How can muscular unloading be beneficial if the concept of strength training is to train (not relax) the muscles? .
Also, what mechanically transpires during fast movement that does NOT transpire during slow movement? Speed proponents are unable to respond rationally, often substituting mystical terminology, gut hunches, beliefs, and hypotheses for fact. Muscles contract - period. Whether you move quickly or slowly, their job is to generate or resist force (resisting force via contraction), regardless of speed. And, as stated, it is force that produces speed and acceleration.
Safety.
The faster you move the greater the risk of injury. Moving a light weight explosively is just as dangerous as moving a 1RM slowly (although you may be producing maximum force to move it as quickly as possible). Speed proponents, at least, concur that there remains risk of injury during explosive movement. .
Exercise, however, should not increase any risk, but should increase functional ability to prevent injuries. It is understandable that Olympic lifters and power lifters run the risk due to high forces of lifting a 1RM, but that should not apply to the rest of the population. Many professional athletes have injured themselves from high-speed training, and they are genetic superiors who can better sustain such rigors.