That's a Shannon B strategy (pick the top n moves and only examine them each time) rather than Shannon A (examine the lot).
One problem is that if you could pick the top n moves easily and reliably, you won't need to do the search, you'd just set n := 1 and have the best move.
The more serious problem is that in Chess, it turned out that trying to work out which were the best six or ten or whatever moves took more time - and was much less reliable - than just looking effectively at them all (typically thirty-odd of them) using an alpha-beta search ('I know this move is worse than the best, and I don't need to know just how much worse, so I won't bother to find out') and other optimisations.
In Go, the number of moves available each time is much larger and the depths you need to search are much greater, so that doesn't get you past a certain strength.
Hence using 'you've seen lots of positions and seen the outcomes, what do you think is best neural network?' approach that also worked for Backgammon.