I have come with a theory as to why men play with female characters in single-player or multiplayer games.
The explanation is basically in Pygmalion's tale. Men are rational yet idealistic by nature, so when young, men fantasize about becoming an ideal (generally muscular) man, and so always pick men in games, as in this way they can build that man and project onto him.
When these young men mature, they'll already have planned how they can become the ideal man they envision, so it is unneeded to project onto a male game character anymore.
When mature, however, men seek a 3DPD hole to mate, and discover that 3DPD holes are not ideal, or even close to be, so by the freedom that games give men, they create their ideal female, and parade her around as their trophy, an exclusive trophy that cannot be touched by no other than that male who created her.
And so, the male becomes enamored by the character he created. This is why a common justification for playing with female characters is "I'd rather stare at a female's ass than a male's ass", because men wish to contemplate their ideal female, crafted by their own hands. This is also the same logic behind why AI art generation is so talked about and used by young men, because it gives men even more freedom than a game to create their ideal female.