Black could always move the rook to a1 before promoting the pawn. It forces a trade, but still leaves black with an advantage.
If white moves his knight to g2, check with the bishop at g3 also gets him another pawn and opens up the king's defenses a little.
White could also take the bishop at f4 with the pawn, but that would just lead to a discovered check.
Given, moving the bishop to b4 does give a better outcome if white moves the king back to row 1. Thanks for walking me through it!