As I wrote long ago (but now sadly cannot find), I generally regard most of the efforts to draw a direct connection between x trait and y survival benefit as being less about science and more about the attitudes on those who insist on such correlations. I am a big believer in Gould's theory that evolution is complicated, with lots of complicated tradeoffs, and isolating particular traits to find specific correlations is generally not useful. We can look at a package and say "hey, that particular orgnaism seems to have achieved a good balance of trade offs" or "this set of things makes sense when playing the odds." But the direct cause and effect for a particular trait (like menstruation) ends up being a just so story with no proof. That may be fun speculation, but it ain't science -- and the cause of science is made worse when people insist on presenting such things as immutable fact.
What we do know is that human beings in their mating habits are both substantially different, but also have considerable overlap with, our closest primate relatives (chimapnzees, great apes or orgutans). The tradeoffs for things such as a bigger brain case and upright posture seem to have come with a general package of things other mamals don't have. Nor is it possible to really distinguish which are learned behaviors and which are genetic behaviors. Human mating habits at times resemble our promiscuous chimp relatives, sometimes our monogamous oragutan relatives, and sometimes our "dominant-male-with-a-harem-that-is-not-always-faithful" great ape relatives.
The limitations of fossil evidence make it impossible to know when menstruation crept into human evolution, and what relationship it might have with other traits. Complex stories like the above may explain at some level how the package of traits humans evolved worked out and why it has proven so successful over time. Or they might be no better than the story that we have winter because Persophene ate pomegranite seeds while visiting with Hades.