Why can't a piece (that isn't a pawn) capture en passant? Why can't a piece (that isn't a pawn) capture en passant? When a pawn makes a two-square move, the en passant rule says that on the next move, any pawn that could have captured it on the single-advance square may do so.

So why doesn't the rule allow a non-pawn piece that could have captured it on the single-advance square to do the same? For instance, in the position

[fen "7k/8/8/8/2n5/8/P7/7K w - - 0 1"]

1.a4


why isn't the knight allowed to respond 1...Nxa3?
I believe the en passant rule is designed to cope with the fact that pawns do not move backwards, hence if the en passant rule did not exists you could have a lot of blocked positions, making play slower and probably more drawish.

Differently from pawns, pieces can move backwards, so the black Knight in your example still has the possibility to move backward and stop/capture the white a pawn. Therefore no need of allowing the en passant rule for pieces.

Said that, there is in a special case a sort of en passant like rule for pieces: castling is not allowed if an opponent's piece controls one of the squares that the King would go through while castling. You can see that as a sort of threat of hitting the King "en passant" during the castling move.

At a large extent chess rules are what they are because they resisted the test of time and made an interesting game. Same goes for pawn moves. The 2-step move from the pawn initial position did not exist either from the beginning, it was introduced later to make play faster and more dynamic; the en passant rule was likely introduced shortly afterwards to avoid large pawns blockades.