This gambit can be very effective if played by booked up players against unprepared/lower ranked opponents -- particularly in rapid style games. Yes, if you're a titled player, you can safely play the 4. Bf4 Qb4+ lines. But if you're a 1700 playing against a 2000, you are probably going to get wacked. There are so many tricks to that line, that if you are underprepared, black can take advantage. I know this from personal experience :)
Another thing to keep in mind is many white players who start off with d4 are looking for a positional/strategic game. The 4. Bf4 response to this gambit allows black to immediately change the game to a tactical nightmare for white.
After losing 2x to higher rated players who know this opening far better than I do, I have switched up responses and have been very happy with results.
The point is that all of Black's tricks are now blunted by the fact that he has to tie down his queen to defending c6 (his best move is the sad Qd8). White continues development with Bf4, eventually castle queen side, put a rook on g1, and a clear advantage without having to worry about anything.
Much simpler solution than knowing every single tactical line associated with 4. Bf4.
I agree with your statement, maybe for an amateur white player its better to choose an easy way to get an advantage with playing 4.Nc3 to avoid all the complications arising in the main lines after 4.Bf4.
But has White really a "clear" advantage in the theory line youve showed...lets go a little bit further...
In my opinion white has a slight edge here and maybe this not the kind of position a gambit player is looking for, but i dont see a "clear" advantage.
Maybe you can improve the position for white.

This gambit can be very effective if played by booked up players against unprepared/lower ranked opponents -- particularly in rapid style games. Yes, if you're a titled player, you can safely play the 4. Bf4 Qb4+ lines. But if you're a 1700 playing against a 2000, you are probably going to get wacked. There are so many tricks to that line, that if you are underprepared, black can take advantage. I know this from personal experience :)
Another thing to keep in mind is many white players who start off with d4 are looking for a positional/strategic game. The 4. Bf4 response to this gambit allows black to immediately change the game to a tactical nightmare for white.
After losing 2x to higher rated players who know this opening far better than I do, I have switched up responses and have been very happy with results.
The point is that all of Black's tricks are now blunted by the fact that he has to tie down his queen to defending c6 (his best move is the sad Qd8). White continues development with Bf4, eventually castle queen side, put a rook on g1, and a clear advantage without having to worry about anything.
Much simpler solution than knowing every single tactical line associated with 4. Bf4.