Capturing (almost) free piece by King Here's a position in a chess puzzle:

[Title "White to move"]
[fen "5rk1/p7/Q1n3pp/3q1p1n/2B2P2/4P2P/P5rK/R4R2 w - - 0 1"]


The rook had captured a pawn, resulting in a check. The rook is supported by the Queen, but the Queen itself is pinned by the bishop and hence will not be able to protect the rook if the King takes it.

Shouldn't King-captures-Rook be a valid move in this case?
No, absolutely not. You are putting your king in check first from the Qd5.

If you think about this way: Who could take the other king first since that really is what checkmate is? In this case, Kxg2 Qxg2 captured the white king first, and only after would Bxg8 take the black king...White lost the king first.

Your thought also does not hold up to logic: White makes an illegal move, so black cannot?