I made a very similar variant a long time ago except that I decided if your king died you just elect a new king. So you swap any of your existing pieces on the board for a king.
The winner again was the whoever was the only one left with material on the board. You can still have drawn games, e.g. if both sides have just a king left or not enough material to force the player to lose his king. (There is however no such thing as stalemate, it would be a win for the player whose opponent was forced to put their king en-prise).
One can, of course, capture a defended queen with their king then if the king is recaptured, swap it for one of their pawns.
(In an endgame you might want to swap a minor piece for the king to enable a pawn to get promoted to a queen).
I wanted to invent a variant called SMESS for people who like freedom and not worrying about their King all the time. It is exactly the same as chess except the King is a normal piece, there is no such thing as check and the King can be taken like any other piece, pawns still queen; to win just be the last guy with a piece on the board.