^ Ok Jirin
, I get that. Good arguments for the longterm. Not to naysay, but here's where other things come in:
Mortality rate - you're assuming a steady curve, when in Starfleet, it can also spike in either direction due to unforseen circumstances: Borg assimilation, spacetime anomaly, political differences, virus, or alien insurrection. Each and every crewmember on the ship was vital to its survival, since the Delta Quadrant offered so many interesting and surprising new ways to destroy a starship and crew.
At any moment you might be facing the loss of half your crew. The Displaced aliens could just have easily beamed them into space and cut the risk of losing the ship to a fraction of a percent. The Devore could easily have made off with 90% of their crew in irons, but voluntarily pulled off due to the loss of credibility Voyager eventually represented.
My argument is not theoretical but in fact, a very real and pressing concern to maximize the crew's survivability in the short, medium and long terms. I see what you mean about equilibrium and mine is a worst case scenario. Of course the story was really about the EMH's growing friendship with the crew - and so, his humanity - and how it was putting him through an identity crisis that threatened his very matrix.
Given the risks of starship duty in the DQ, I still believe my hypothetical thought experiment may still have something to it. Not that the "chivalry" aspect could not have worked the other way, it very well could have. But in terms of reproduction? There would be no way to know what tomorrow held in store for each and every one of them. A human male's response might skew toward saving the female, and the female response might - actually I have no idea. In this way, the EMH might have been more PC than male, but more human than PC.
Or maybe this is just gender bias, but reproductive factors drive much
of human behavior.