The most foolish of all approaches is approaching a girl on her own, she has the upper hand and you come at her from a position of weakness.
What makes this even worse for guys with standards that go beyond just appearance is that you never get the chance to assess her character and she feels no need to even display this, by her standard she already considers you cheap and worthless and rightly so.
The best approach is the group approach, not the type of approach that includes flirting or anything overt, just a simple light hearted joke at them or banter to get the ball rolling, no serious conversations or lectures.
In the old days it was me and my best friend against usually 5 or more in any event, with this type of approach all the cards are in our hands.
An element of mystery is created were each girl instead of being convinced you want her which is the case in 1v1 approach and she jumps on her high horse, curiosity makes them all jump off and wonder who each guy wants, they begin to compete against each other!.
The benefit of this is numerous, everyone's guard is down, you get to know all of them reasonably well if your observant and the upside is that you can pick any girl you want from the group at will and the social proof is already done in the banter phase.
Approaching a single girl for us was the worst thing you could do unless she explicitly and unequivocally signals to you in which case you wouldn't even want her anyway.
Giving a girl the green signal (by approaching her alone) before you have even assessed her character, personality, upbringing and intellect is suicidal and bad rep.
This is something that only the inexperienced fools do, because with groups rejection doesn't exist, it only exists in individual foolish solo missions where she gets on her high horse.
I've been in enough situations like that to know there is no real element of mystery in most cases. Women have good intuition and men's body language usually betrays them.
Most girls have been in a group setting in which guys have approached and the girls (friends) know WHO he really likes, in fact if we all think he is a catch, we secretly gesture to her to show a bit of interest and engage in with the banter ect.
We women are subtle, so you are here thinking that we have no idea, but 98% of the time we do and the better we think a guy is the more we are enthusiastic for the sake of the friend we think he likes. I actually remember, a couple of years ago, two guys approached and we all instinctively realised one really liked a particular friend of ours. When the guys went to get water, we all turned to our friend and told her to stop being overly quiet and for her to say something, so he doesn't lose interest!
I don't know what group of girls you have approached, but from what I have seen very rarely do women compete with each other in this situation for the simple fact that competing is fruitless, as at that point the friendship group have already identified or guessed who they think the guy really likes. So any bitterness or jealousy would have to be kept under wraps. I can imagine for some women the jealousy is alive and kicking, but they just have to just suck it up at that point.
Because why compete on a forgone conclusion?
But apart from that I agree with you. Women tend to respond better in group situations. It helps us gauge his social skills and confidence which is important. So the man you may not have found to be physically appealing, starts to look better because of his wit and intelligence.
However, another point I have to add is also from my personal experience is that women may feel a sense of shame rejecting a guy when he came across as polite and bantered with everyone. Also, depending on how close a female friendship is, friends will look at you a certain way and would secretly gesture to you to give him a chance , when they think he is a good man.
It is awkward to reject a guy even if it is the nicest way possible infront of everyone. I did that once, but I was incredibly young and naive.
Next time you are in this situation, really focus on the secret glances the girls give each other. Actually pay attention.