First of all, could focusing on eccentric movement make you stronger? Yes. However, if you only use this method then you will lack the necessary strength to concentrically move the weight. It takes more “energy” to contract a muscle via actin and myosin, therefore shortening the muscle. During a concentric contraction, muscle fibers slide across each other, pulling the Z-lines together. During an eccentric contraction, the filaments slide past each other the opposite way, though the actual movement of the myosin heads during an eccentric contraction is not known.
Therefore, we are able to resist more weight eccentrically because we have a greater ability to simply resist the load. However, when doing so under heavy eccentric loads we also create an environment where there is a great deal of muscular “damage”. Essentially we have the ability to damage muscle more under eccentric load, but this may not be a good thing as we may be sore for 3-4 days; impairing our future training sessions. Anyone who has done negative chin-ups with significant volume can speak to this fact. Cue in picture of T-rex making a bed.
Secondly, your movement patterns or “mind-muscle connection” will get better under appropriate load with proper coaching. Moving slower DOES NOT guarantee someone will move better or more efficiently. If you have a crappy coach then I don’t care how slow or deliberate you move, it won’t get better. Your coach needs to strive for perfection!
Lastly, their theory that your power will increase. Let’s be logical and think about this. Strength=LoadxDistance, Power=LoadxDistance/Time. So power is dependent on strength! Using pauses (isometrics) or eccentric training in and of itself does not mean you will get stronger. Also, if you are interested in power I’m assuming you are an athlete or competitive Olympic lifter. To be powerful you must be able to produce large amounts of concentric force, as that is what power is, moving large loads over long distances quickly! Because the limiting factor is how much weight you can concentrically move, not how much weight you can resist. Training eccentrics for power is just silly.
In summary there is use for eccentric work, pause (isometric) work and tempo work as an accessory to improving your strength. Key word ACCESSORY! These methods are used by the world’s best but only when they get to the point where they are needed. The vast majority of the training world can use regular strength training for a long time to get strong. When a simple set of 5x5 is no longer enough to drive adaptation, then you should choose to add another method that could drive progress. Do not use eccentric, isometric or tempo work as your primary strength driver as you will not be getting as strong as quickly as possible. You will be missing your gainzz.