Sure, I know what you're thinking. You're thinking it's a great form of functional training and a good exercise for eyehand coordination. These are two very valid points of view, but there is more to this story.
When you shadowbox, you are watching your own technique. You want to be fast -- but, at the same time, you do not want to telegraph your punches and kicks to your opponent. So you watch. Do you drop your shoulder when you punch? Do you shift your weight or stance before kicking?
Becoming aware of these things can make you a better fighter both offensively and defensively:
- offensively because you stop telegraphing your techniques, and
- defensively (even more importantly) because you can anticipate your opponent's movements by knowing what techniques can be thrown effectively from specific body positions.
Speed is always important, but being able to read your opponent: priceless.