I have the same concern as Daniel Kokotajlo, but for a different reason.
Mr Malmesbury considers the gradual extinction of genders beyond 2, but he never mentions the injection of fertile new genders into the population through mutations.
In order to make the case convincing case for unique suitability of exactly two genders, we should look for reasons why systems with three or more genders would be unstable. Here is a hint: consider a third gender entering into an established species with two genders: one with a huge gametes, the other with tiny gametes. Where does the gamete size of the new entry fit in?
I’ve always felt the Fisherian runaway hypothesis begs the (second order) question:
The first order question (for the scenario here) is—Why don’t the male bird head plumage continue to grow indefinitely longer from generation to generation? This one is easy. At some point the plumage would become so impractical as to make mating impossible.
The second order question is harder: Why is it that some species get away with remarkably impractical features (the peacock comes quickly to mind), while other species appear to be pretty close to a local maximum in adaptation?
I suppose that a scarcity of predators and a generous environment ought to be part of the story for the most flamboyantly maladaptive species. But has this been empirically verified? And are their other considerations at work?