Basically Sheiko works so well as it was researched and tested on 0000's of Russian athletes...
The research found that for most beginner and intermediate lifters the most effective way of building strength is through building volume. Volume will build muscular strength, but most importantly it will reinforce the motor patterns, building neural efficiency and technical excellence. It is here that lifters will build the greatest gains initially. The anecdote used is that of a new lifter. A newbie to the gym will experience incredible strength gains in the first 6-8 weeks of training. Many believe that this is due to muscular growth prompted by new stimulus. While muscular growth occurs, the research (muscle biopsy, for example) showed that it was not as significant as many assumed. The major gains are made through building motor patterns which increase neural/muscular efficiency, which results in greater power output.
The realization that follows is that training the movement can be more productive than training the muscles- by this I mean an emphasis on the powerlifting movements, instead of focusing on muscle groups will prioritize what builds optimal strength.