Some of it has to be psychological. Instead of grabbing the Bishop at move 4, and preparing to accept another piece the next move, Black says "No, thank you" and creates a bit of a gambit, himself. So, Black exchanges the opportunity for a "won" game with the chance to be a pawn down, with little objective compensation.
Huh?
perrypawnpusher - PrestonRFD
Italian Game Classic", Chess.com, 2019
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
4...Ke7
The Jerome Gambit Declined, and probably not in the best way.
The Database has 49 games with this position, with White scoring 70%, including perrypawnpusher - walkinthe spirit, blitz, FICS, 2009 (1-0, 24) and perrypawnpusher - walkinthespirit, blitz, FICS, 2010 (1-0, 34).
Stronger appears to be 4...Kf8, which appears 312 times in The Database, and against which White has scored 56%.
By comparison, based on almost 14,500 games in The Database, White scores only 46% with 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7.
So - Black gives up something by refusing to accept the sacrifice, but the lesson of Geoff Chandler's "blunder table" is that the pawn Black offers in return is not much of a loss on his part. In the meanwhile White is forced to create a plan.
5.Bb3
Certainly 5.Bxg8, instead, is worth a look: it scores 8-0 in The Database. I gave it a glance before moving my Bishop, but was needlessly worried about 5...Qxg8, with two heavy pieces backing two pawns aimed at the future home of my King.
If the Bishop is not exchanged, where should it go? On any given day, computers seem to prefer 5.Bd5 or 5.Bc4, although I can not figure out what advantage those moves have over the full retreat to b3.
The Database confirms that Black has succeeded in one of his goals, that of confusing White. The eleven 5th move responses include 5.Bb3, 5.c3, 5.Bc4, 5.d3, 5.d4, 5.Bd5, 5.Nxe5, 5.0-0, 5.Ng5, 5.Bxg8 and 5.Bh5.
5...Nf6
Sensible, predictable and, according to the computer, wrong.
6.Nc3
I know that I am supposed to know all about the Jerome Gambit, so it is a bit embarassing to see this is at least a small error, as well. White should grab the pawn at e5, initiating the "fork trick": 6.Nxe5 Nxe5 7.d4 when he will get back either the piece at c5 or the one at e5. (I can console myself that there are no game examples of 6.Nxe5 in The Database. I should add this move to my "Jerome Gambit Secrets" posts.)
6...d6 7.h3
This is a boring move, designed mostly to prevent ...Bg4 as an aid to a possible ...Nd4. It was disappointing to come to grips with the realization that my advantage in the game was mostly the extra f-pawn, which wasn't going to advance any time soon. So, my plan became: small moves, small ideas, let him take the leap.
7...Re8 8.d3 Kf8 9.O-O Be6
After the game, Stockfish recommended now that White play 10.Bxe6 Rxe6 11.Ng5 Re8 12.Nd5, with a complicated tactical line.
No matter. After
10.Bg5
Black lost on time.
I am not sure why. Perhaps: the real world.
Strange game, right to the end.
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