Puzzles should gain material against all replies, not just because the opponent makes bad responses. As it is your tactic is unsolvable.
As for whether it comes up often, people don't normally weaken their kingside by advancing their pawns like that as they get stronger.
Here's a nice checkmate puzzle (of a strategy I used in one of my games). Can you see it? This is a four move checkmate for black. If you manage to solve it, do you think that this strategy often goes unnoticed; because I have checkmated in a similar way to this many times.