Most lifters today focus too much on lower body strength. This seems to be a byproduct of the removal of the press from Olympic lifting back in 1972. People tend to forget that we use the whole body when we lift, not just everything below the belly bottom.
Research has showed that the best way to improve the snatch and the clean and jerk is to do the lifts or versions of the lifts often. Not to squat. The squat is used as a way to build strength in the lower body but in general has low transfer to Olympic lifting(Rykov study shows a factor of 0,55 for the back squat and 0,77 for the front squat). As a general rule ones snatch should be in the range of 0,6 or higher of ones best squat. The ratio for C&J=0,8 of the squat. Someone that squats 200kg and snatches 100kg should not work on improving his squat, he should improve his snatch. In order to use the full body we also need strength in our upper body. Strong lower and upper back, a stable core and a strong shoulder girdle. Different kind of pulls and rowing motions for upper back, special low back exercises and press movements for shoulder girdle is just as important as squatting for general strength of the lifter.
On the upper pictures one can see Mr. Tommy Kono, One of the best lifters of all time. Kono knew the value of symmetry and even won Mr. Olympia while still active as a lifter. On the next picture we can see Yurik Vardanyan, One other of the greatest lifters. Notice the symmetry of Mr. Vardanyan, Upper body matches lower body. Some modern examples of lifters that has understood the value of symmetry and upper body strength are: Aurimas Didzbalis from Lithuania, Lu Xiaojun from China(as a general rule Chinese lifters focus a lot on symmetry and do not neglect upper body training). Remember Leonid Taranenkos 266 C&J. He used every muscle in his body make that lift. Taranenko used to do the Olympic press, after 230kg he felt that it was no longer needed to press. He was strong enough!
It has been said before a chain is not stronger than its weakest link, this applies not just to weightlifting!