A lot of you are interested in the details. What does the science and theories say? This page is designed to answer those questions. Start with this video.
details, details, details
A couple of things are left out of the video. One of the most important things regarding power generation is pedal speed. The power at the pedal at any time is calculated by looking at the force on the pedal (in the direction the pedal is traveling) times the speed of the pedal. The problem is if the pedal is moving 100 mph it is not possible for us to put any force on the pedal. Before we can put any force on the pedal we have to get the foot up to the speed of the pedal. If we don't do that then we put negative force on the pedal and that slows us down. So, in general, the faster the pedal is moving the harder it is to apply force to the pedal. But, slow pedal speeds are not very powerful either. We can put the maximum amount of force on the pedal when it is stopped but our power calculates to zero because pedal speed is zero. At very low pedal speeds power is reduced and at very high pedal speeds power is reduced.
The other issue is endurance. If we are only going to be pedaling hard for 30 seconds (a sprinter for instance) we need a much higher pedal speed for max power than if we are going to be at power for 30 minutes or 5 hours. The riders problem comes from figuring out where the sweet spot is for them for the kind of racing they do and for how fit they are. One way you can watch this in action is to watch your power meter as you accelerate from a stop to a very high cadence - you should watch the power increase as the cadence comes up and then decrease as you pass the sweet spot. Realize this sweet spot is for this short duration test and probably won't apply to the kind of racing you do. The idea of such a test is simply to illustrate the principle.
The above also relates to short cranks. For the same cadence short cranks reduce pedal speed. Aside from the knee leverage issue this also probably accounts for why shorter cranks don't lose power since we can increase the force on the pedal to make up for the reduced crank leverage.
Anyhow, I think you should understand by now that there are a lot of things involved in devloping power and if everything isn't optimum then it is not possible for us to reach our full potential. Figuring out what is best for each rider is not easy. Next time someone tells you they have a formula for crank length or some bike fit issue just ask them what science it is based on. The silence will be deafening.
This video reinforces what was discussed in the above video about why we pedal as we do because of how we learned as kids. Once that pattern is ingrained it isn't going to change just because you attach your feet to the pedals.