Would this arrangement be a really twisted version of "Survival of the Fittest?"
Not really, as the loser both 'survives', and even gets to pass on his (now her) genes (which is the whole point of 'survival of the fittest').
Though, I must admit it would be darkly humorous to see how straw-feminists (the ones who don't actually want equality, just a reversal of the current paradigm) and SJWs would react to this world.
Wager your egg, and duel!The one who loses...Will be turned into a woman!And that had became the new law for this continent......Eerghhhhhhhhhh!And humanity could continue to live on in spite of the curse.