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I've known the en passant rule for 30 years but...

I've known the en passant rule for 30 years but, how come only pawns can take en passant?

Note that kings can't castle through check, which is a case of "en passant"

Bxa3 e.p. sounds strange, but why does it?
I understand it'd also mean one could take a long shot piece en passant, which would definitely change the game.

I guess my question, is when , why and by who was this rule implemented?

My question
In the shatrang game, pawns could only move one square at a time. Then came the rule that a pawn could move either one or two squares from its initial position. As that would provide an unfair advantage to the pawn on the initial position versus a pawn advanced to the 5th row, the en passant rule was introduced so that the pawn on the 5th row could take the advancing pawn on the 7th row as if it had only moved one square instead of two squares.
I think the en passant rule with pawns so that
1: players could not easily obtain passed pawns
2: players could not force the game to be closed, making for boring game
The same think occurred to me recently. The "en passant" rule makes total sense, but I don't see a reason why other pieces can't do it. This rule is a way to say that the double step of the pawn is just a way to speed up the game and not a way to pass through controled squares without being en prise. So it would be logical if any piece could do it.
Maybe there are historians of the game around here who can tell us if it has been essayed at some point. I think it would be interesting to try it.
I remember when I first started playing chess, someone captured my rook by "en passant."
When I first started playing chess, someone told me in the beginning of the game either one pawn advances two squares or two pawns advance one square each.

Kings could be captured freely as well, so one unnoticed exposed King through check ended the game.
The king not being able to castle through check does seem like a form of en passant. This is the connection I made though

Pawns usually move one square
Kings usually move one square
Under certain circumstances, pawns can move 2 squares
Under certain circumstances, kings can move 2 squares
In these circumstances, it would be able to bypass an attacked square without any dangers, except for said special rule

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