In the Berlin Defense(ruy lopez), why has the Ne7 Ng6 plan gone out of fashion? 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: 


So - Kramnik
Maze - Smith
Caruana - Dominguez
Caruana - Carlsen
Nakamura - Topalov