Maybe if you're defining "good" as playing off +2 and "great" as playing off +5. Then you can convince me that the incremental improvement is mostly course management, putting, and a spectacular short game.
For the rest of us schlubs, it's about full shot ball striking. The reason I beat my 12-15 hcp buddies is that I don't lay the sod over the ball once or twice a round. I don't top a 3-wood, or skull a mid-iron. I don't blade a wedge over the green from 60 yards, and I'm not flirting with the woods on every 3d drive. In short, it's because my ball striking, while not great by ANY means, is more solid and consistent than theirs, and as a result, my 32ish putts nets me 78 or 80, while their same 32ish putts nets them 90+ more often than not.....
......likewise, the reason my 2-3 hcp buddies beat me is that they're hitting another couple of greens and thegreens they do hit result in shorter birdie putts. Again, ball striking.
But just figuring that 2 putting is half of par tells me its half the game or what you use more than any other club. What clubs get trashed by pros more than any other? Drivers and putters...keeps the pro shops in business$$$