Ajian, that is a totally different line and not your initial question. Understand my confusion.
Black doesn't have to play 9...e6, there are other moves like 9...Bd5.
Looking at the 9...e6 line for a moment, there might be 11...Be4 12.Rb2 c6, with a solid wall. My engine also likes 12...Qd5 but I don't know.
Your line with g6-h6-Kg8 looks a little awkward for black. Costs time.
by the way if black plays Bd5 then Bf3 might give the white attack more force with e6 breaks coming in. Here's a game I played off chess.com
Well, as long as any questions you had were answered then.