I'm in general agreement, but one must remember that culture is always important. For instance, in the west a girl approaching a boy isn't really seen as strange 9/10, it has little to any impact on her social standing, but depending on where you live in the world this could be a major taboo that's strictly enforced socially if not perhaps legally. Girls are more social than dudes, it's how they seem to be wired (eg. they're better at learning through spoken instruction, dudes learn best by making connections to visual events i.e. they learn faster with hands-on teaching and visual aids over just spoken instruction), but the social standing within any group is affected by an approach as well as the outcome of the approach.
From a general standpoint the approacher is the one taking the higher risk, as if they get rejected others will feel better/find it easier to reject them as someone finally did it first. Fascinating facet of human behavior is that in general people don't wanna do something negative "first" if they've been properly civilized. They wait for someone else to do it "first" then the cascade starts (could be an introvert vs. extrovert thing). Thus, if you get rejected, your social standing will at the very least be called into question. Of course, *how* you were rejected will also matter. The harsher the rejection, the more potential social damage is done. "Polite" rejections won't deal much damage, and them already being taken is about as polite as you can get. This is why a girl will say she has a boyfriend, even if this is not true if rejecting a dude to minimize damage. I would assume guys do this too, I know it's what I'd say to a girl I didn't wanna date (real reason: really bad attitude and subpar looks, but saying this is a "harsh" rejection and is thus kinda mean).
Damage potential is mitigated if in the company of "friends" who can reassure you that your standing among them hasn't been damaged. Thus re-emboldened, you can then initiate another approach or approach a different person hoping for a more positive result which will be met with the accolades and congratulations of said friends. The approachee is the lucky one, as by simply being approached their social standing goes up. After all, if this stranger/other person is into them they must have some positive qualities. Assessment by other parties goes up, preselection is a thing. The fact that you got "selected" makes other people reassess and want to "select" you too. Of course, the approachee, if seeking an approach, is risking their individual ego and pride (especially if they're knowingly doing it). You would obviously adopt a series of behaviors to attract the attention you desire, if you fail to get it then that's a big blow to the ego personally. If that happened to an extrovert I'd imagine the psychic damage would be devastating. Introverts, well, they're already used to being alone.
That's just me overthinking things like usual though, so there's always that.