I think that if the developer isn't actively trying to say something about men, women, or specific relationships between the two (or going even further, trans people and such), they should allow the option to change. It gives a player who DOES prefer to play as a specific gender more enjoyment without hurting anyone (unless the modellers are just really lazy). Consider trans people again, who literally fight tooth and nail every day to be perceived as their gender in spite of bad luck during birth. Should they be forced to play a story as an avatar that makes them personally uncomfortable just because the developer is lazy? No, I don't think so, especially because it is so easy to make a gender flip, easier if you take the "Shepard" route and have them have the same name.
Again, though, if a game has something to say that can only be said with a specific gender, then yeah, no problem! Although, with enough creativity (and time), I find many of those games could still have a gender flip, and simply have it divert course in a different way for each. Perhaps a military shooter set during a time where women aren't allowed in active combat could have a male player out in the field taking down Racist McBadguy, while a female one is back at the base when it gets attacked. You could even re-use the levels too, having male player fight his way back to the base, and have female player fighting in the field after having escaped the attack on the base. All it would require would be extra level scripting, which from personal experience, is one of the easier things to do.
Also a quick rebuttal against one specific thing: Yahtzee said that it's actually worse for the hero who is rescuing the damsel, because he has to die over and over to save her. That's ridiculous. Unless the plot acknowledges the life system (like in Bio-Shock with the vita-chamber things, most players will assume that it's all one big uninterrupted story. AND second of all, being held against your will or even killed (permanently, I may add) still fucking sucks man! Idk that was just a ridic argument.