It doesn’t matter where they cork it, the difference in density moves the sweet spot further in. The deeper down the barrel one hollows, the more you move the sweet spot, even if you don’t reach it. Basically, corking the barrel of the bat is de-fungoing it.
The way to increase batted ball distance would be to cork the handle of the bat. But the obvious problem there is that it damages the integrity of the wood on the weakest part of the bat, and would definitely lead to more broken bats...