I don't know if anyone ever opined "Never send a pawn to do a job a piece could do..." but the exact opposite is true in the following game. Bill Wall's 11th move improvement over an earlier game he played leads to an even faster win.
Wall,B - FJBS
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
4...Kxf7 5.Nxe5+ Nxe5 6.d4 Bb4+
As befits the wackiness of the Jerome Gambit, this idea was seen in a game played 10 years earlier in a Jerome Gambit thematic tournament featuring two double-forfeits.
Bill has also faced 7...Be7 8.dxe5 Nh6 9.Qf3+ Ke6 10.Bxh6 gxh6 11.Qf5 checkmate, Wall,B - ChrSav, FICS, 2010.
An interesting idea: 7...Qh4 instead.
Stronger than 8.bxc3, as in HauntedKnight - OneNoTrump
blitz, FICS, 2011 (1-0, 10) and shugart - chingching
blitz, FICS, 2012 (1-0, 25).
Or 8...Nc6 9.d5 (9.0-0 Qf6 10.e5 Qg6 11.Qf3+ Ke8 12.Nb5 Kd8 13.Qf8+ Qe8 14.Qxe8+ Kxe8 15.Nxc7+ Ke7 16.Nxa8 Nxd4 17.Bg5+ Ke6 18.Nc7+ Kxe5 19.Rae1+ Kd6 20.Bf4+ Kc6 21.Rc1+ Kb6 22.Nd5+ Kb5 23.Rxc8 Ne6 24.a4+ Kxa4 25.Ra1+ Kb3 26.Be5 Black resigned, Wall,B - Caynaboos, FICS, 2011) 9...Ne5 10.f4 Ng6 11.h4 Nxh4 12.Qh5+ g6 13.Qxh4 Qxh4+ 14.Rxh4 Nf6 15.e5 Ne8 16.Be3 c6 17.0-0-0 d6 18.e6+ Ke7 19.g4 Nf6 20.f5 gxf5 21.gxf5 cxd5 22.Bg5 a6 23.Nxd5+ Kf8 24.Bxf6 Rg8 25.Rxh7 b5 26.Be7+ Ke8 27.Nf6 checkmate, Wall,B - ChessFlower, PlayChess.com, 2012.
9...d6 was AsceticKingK9 - Luke Warm, Jerome Gambit Thematic Tournament, ChessWorld, 2011 (1-0, 16). Beware the "Jerome pawns"!
10.e5 Ne8 11.f4
This addition to the pawn chain is an improvement over 11.Qf3+ (but still: 11...Kg8 12.Qd5+ Kf8 13.Be3 a6 14.Rae1 c6 15.Qb3 d5 16.f4 Kg8 17.f5 Nh4 18.Qc2 g6 19.f6 Be6? (19...Kf7 20.Na4) 20.Bg5 Qb6 21.Bxh4 Qxd4+ 22.Bf2 Qf4 23.Ne2 Qc4 24.Qd2 Qxa2 25.Nd4 Bf5 26.Nxf5 gxf5 27.Qg5+ Kf7 28.e6+ Kf8 29.Bc5+ Nd6 30.Bxd6+ Ke8 31.f7 checkmate, Wall,B - Boris, SparkChess.com 2012)
Planning to castle-by-hand.
For better or worse Black had to continue with 12...Kg8, returning the piece.
13.Qb3+ d5 14.exd6+ Black resigned
White will deliver checkmate in a couple of moves.