It seems that after 9. h3 or 9. Nc3, black usually plays Ke8, Bd7, h6, and sometimes Ne7. My question is: why isn't 9... Ne7 played more often, with the plan of putting the Knight on g6?
Situation:
[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. O-O Nxe4 5. d4 Nd6 6. Bxc6 dxc6 7. dxe5 Nf5 8. Qxd8+ Kxd8
One of the reasons could be that the knight on f5 is already developed. Probably it doesn't appeal to many players to spend 2 tempi to reposition the knight, while black is already slightly behind in development.
Futhermore, many alternative setups are possible and perfectly playable: Ke8, Bd7 and Kc8, etc...
However, it seems that an early Ne7 recently regained some of its popularity:
