Greco Defence: 1.e4 e5, 2.Nf3 Qf6

according to my pgn downloads i had been 6-1 against the greco defense before learning, after googling moves from the game below, that it had a name.
in 5/6 of these wins i played 3.d4.
http://www.chess.com/livechess/game?id=536841940
my one loss against this opening was an embarrassing fool's mate, the exact nature of which is left as an exercise.

This isn't that bad, I just played it with good results.
For instance,
This is how the game went, and black is doing just well and even took the luxury of capturing a central pawn.
If 3.Nc3,
for example. So I don't see where's the terrible flaw on this oppening if one as black simply plays natural developing movements. Of course bizarre reponces as 3.(...)c6?! won't do any good, but that is also true for any other open game.

2.Qf6 is really bad.
However 2. Qe7 is perfectly playable. Of course the dsB will develop to g7.
even this is a stretch. In general, early g6 lines in both the italian and the ruy lopez are on the slow side and require some precise play if white plays the critical lines, playing qe7 adds another tempo "lost" in an already slow system.
how is black better?
I think the better moves for white here are 5… Nd1 or 6…Nxd3. I think that if white initiates the exchange as you have, the uncastled king on the open file renders white's development advantage rather moot. It winds up looking like an even game. I think with either of the two knight moves, white winds up with the advantage.