The Jerome Gambit is not a guaranteed win.
Indeed, The Database has 36,195 games starting with 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+, and White scores 53%.
Of course, some individual Jerome Gambiteers score much better. (I score 81% in my games, and I am, by no means, the most successful.)
Players also have good days and bad days with the opening.
The following game reminds me of fight manager Joe Jacobs, who in 1935 lamented I should have stood in bed.
Chioborra - Duckfest
Jerome Gambit Practice Tournament, Chess.com, 2023
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
4...Kxf7 5.Nxe5+ Nxe5 6.Qh5+ Ke6
7.Qf5+
If Readers want to explore an alternative to White's 7th move, Yury V. Bukayev has given a lot of attention to 7.Qh3+. You can use search function to find all of his important analytical researches and games including the latest part:
"JG: The New in Its Opening Theory, in Its Psychology (Part 14)".Moreover, Yury has given some attention to 7.f4:"Was H.Nakamura Right? Is JG ‘Unbreakable’, Is EG ‘Legendary’ For Beginners’ Games? (Part 2)".
7...Kd6 8.c3
This move is a bit slow. It is seen in 167 games in The Database, with White scoring 46%.
8...Qf6 9.Qxf6+
It is unfortunate that White has to exchange Queens, as it dampens his attacking chances.
9...Nxf6
I realize that White has d2-d4 coming, and that Black's King is akwardly placed, but the second player is clearly better.
Once again, the first player will have to press and be aware of chances as they come. As a start, 10.d4 would block the enemy's Bishop's pressure along the a7-g1 diagonal and allow, after castling, f2-f4.
10.O-O
I suspect that White expected his opponent's next move, but figured that his Queenside play would be adequate.
10...Nd3 11.b4 Bb6 12.c4 c5
13.b5
There is not much play left here.
13...Nxe4 14.Ba3 a6 15.f3 Ng5 16.bxa6 Rxa6 17.Bc1
Black now attacks the c4 pawn, and from there, the Bishop.
17...Ra4 18.Na3 Kc6 19.f4 Ne6 20.f5 Nd4 21.Nb5 Ne2+ 22.Kh1 Rxc4 23.a4 Nexc1 White resigned