Good Grief...
Well, you were talking as if giving away that Pawn was automatically advantageous to White.
It isn't. It wins time (by luring the Bishop to the vulnerable b4 square) and allows White to quickly build a center with c3 and d4.
If Black plays 3. ... Bb4, White gets those advantages WITHOUT the need to give up a Pawn.
Put it this way...
The Evans Gambit:
The Evans gambit isn't equal, it's imbalanced.
The Evans gambit is a pawn down compared to the other line, although the Evans gambit has a space advantage.
My point is that in the line you've offered, White gets ALL the advantages that the Evans Gambit offers WITHOUT sacrificing a Pawn. In effect, he's playing an Evans Gambit, a Pawn up.
In the Big Database (with players of all strengths included), the Evans scores 47.3% White wins, 18.9% draws, and 33.8% Black wins. Total: 56.75% for White.
In the Small Database (Master games only), Black does better (30/38/32, total 52% for Black) but those numbers are still well inside the "Equal" range.
The line you suggest (1. e4 e5 2. Nf3 Nc6 3. Bc4 Bb4) scores 74.6% White wins, 10% draws and only 16.6% Black wins. Total: 79.4% for White. It isn't in the Masters database at all, since it's so obviously a bad move.
The missing pawn in the Evans gambit is also it's greatest strength, the line I have shown with the pawn still being there as opposed to its absence plays differently to the Evans gambit.
The fact that the Evans gambit is missing a pawn gives it a space advantage as well as an activity advantage that 1.e4 e5 2.nf3 nc6 3.bc4 bb4 4.c3 doesn't have, therefore it isn't necessarily superior to the Evans gambit for white.
Pawns determine space advantage. The missing b-pawn does not add to whites space advantage, The missing b-pawn gives white potential piece activity due to the semi open b-file.
So you recommend giving away all your Pawns?
Not all gambits offer increased activity, although lots do.
Being a pawn down dimishes central control, as having less pawns makes it harder to control the centre, being the Evans gambit's major downside.