>That's the flirting I speak of, the same sort of flirting/friendliness that was originally mentioned
I was responding to the idea that being single or not has some effect on the scenario. Flirting (whether deniable or not) is neither exclusive to single people, nor required to affect the social status of men you interact with.
>It's foolish to assert that female approval matters, but darn it, no one knows why!
It is foolish to assert that the universe exists, but darn it, no one knows why! We observe things, then we develop hypotheses to try to figure out why they are as they are. Then we test those hypotheses to see if they are accurate. The observation does not cease to exist simply because there are no hypotheses that have made it to proven theory.
>In my experience, female approval matters because of the perception of sexual and romantic prowess that it grants to the receiver, especially in the eyes of other men
That may well be the case at a subconscious level. But that doesn't go away because any or all of the people involved are in relationships. I have been married for over a decade. I do not actively seek the attention of women as a result of this fact, but I still treat them the same way, and they are still able to coerce me into doing what they want even though both of us are fully aware that there will be no sex rewards happening.