Why would you castle so early? White's plan is to attack the kingside and you're just putting your king there? Why? Its like running into the middle of a battlefield.
Yea, who would play the #1 move recommended by Stockfish? Don't insult people when you don't have a clue. The king is safer there than he is in the center, and it brings the rook into the defense.
^I'm not sure white has any problems after 4. Ngf3 Bc5. 4. Ngf3 is considerably more common than 4. g3, actually. I guess what you're getting at is that if white intends 5. g3 against anything then it can be a problem because Ng4 is coming, but white can play 5. e5 Nfd7 6. d4 Be7 7. Bd3 which is a position that Karjakin has played several times with white. I doubt he would say 4...Bc5 is a problem at all. Committing to g3, meanwhile, arguably makes the idea of dxe4 and e5 much stronger.