I'll throw my hat in the "ballstriking" ring also. The really bad shots (OB, hazard, 40-yard wormburners) have a much greater impact on score than the occasional missed putt. As those started to go away my handicap went down. In fact, I'd say the remaining bad shots I have left are the reason I'm not sub-5 yet. Over time my short game has been very consistent: consistently streaky, that is.
Obviously all parts of the game contribute to a good score, but better ballstriking will knock off more strokes in less time ... unless you have nothing but free time to play and practice everything.