IMO the idea of staying on top of the ball all started when someone caught on to the fact that most fastballs are missed below the ball. That was before there were so many sinker ball pitchers.
Problem is that at the same time most pitches missed on breaking balls are missed above the ball.
So if a hitter were to actually stay above the ball he would become just another victim of the many who didn't make it because they couldn't hit the curve ball.
The theory of chopping down lacks successful examples. I think some believe it creates more back spin.
Obviously the barrell has to drop initially, but only so the hitter can get it close to on plane with the pitch. The term for this is "squaring up" the ball. The best bat/ball contact is pretty much a head on collision! This is why we see so many high finishes. Also there is no margin for error when chopping down.
Most every pitch is on a downward angle to the plate, I'm amazed that so many people think the way to hit is chopping down at a ball that is going downward. We have told hitters facing a good fastball to stay on top. At the same time we have told hitters facing a good breaking ball to stay below the ball. This is just a mental thing rather than anything physical. But never make contact while chopping down.