This principle is of promoting to what you capture is known as 'contageon'; what you propose is to make all pieces contageous, but only for pawns. (I.e. all other pieces are 'immune'.) I used that rule (borrowed from the historic large Japanese chess variant Maka Dai Dai Shogi) in my variant Werewolf Chess. There the only unorthodox piece (the Werewolf) is contageous, and only Kings are immune. The effect is to make it next to impossible to trade the Werewolves out of the game (and thus revert to normal Chess).
In general having pieces promote when they capture is a very strong deterrent for trading those pieces. This might paralyze the game, especially with FIDE Pawns, which tend to form impenetrable interlocked walls if they are pushed without trading. (In Maka Dai Dai Shogi pawns move and capture straight ahead, so the danger of a stand-off is smaller there.)
So I had an idea for a chess variant which had an additional promotion rule for pawns. Basically, if a pawn captures another piece, it will become the piece it captured. So if you capture a knight, your pawn becomes a knight and so on. Obviously if you capture another pawn you remain a pawn. If you manage to have a passed pawn promote normally then normal promotion rules still apply. I think that would lead to interesting strategies where either you're hesitant to make a trade knowing that you're promoting their pawn, or else on the opposite end if someone has a passed pawn that they want to promote to a queen, if you defend the promotion square with a knight/bishop you can try to force them to promote it down instead. What do you think?