Does white win stalemate-wins chess with optimal play?

Imagine modifying the rules of chess so there is no such thing as check or checkmate. You win simply by capturing the opponent's king. This is not the same as traditional chess: a "stalemate" is now a win, not a draw, because the enemy king is forced to move into check.

It seems plausible that this change might make the game much less drawish -- after all, there are a number of endgame positions which are drawn only because of the stalemate rule.

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"stalemate wins" and "no such thing as check" are not exactly the same thing (can you castle through check? would deadlock ( Diagram 5) be a loss for the player to move?)