ChessVariant:
I think this "protected chess" would be confusing enough without special rules for the pawns. Consider, for example, a position where white has a pawn on d3 and bishops on e4 and f6. Assume that the bishop on f6 is unprotected and moves like a cardinal, giving check to the black king on g8. Now, provided that the d3 pawn is the only piece protecting bishop-e4, black may parry the check by taking this pawn. Be4 now becomes unprotected and moves like a cardinal, so Bf6 is protected and moves like a bishop, and there is no check. I imagine that this kind of chain reaction could become extremely complicated and create some insane tactics - so please, just let the pawns be pawns :-)