But wallflowers stand by the wall because they don't want to be approached.
Those kinds of fears are generally unfounded, but it's difficult to prove to yourself that they're unfounded without actually interacting with people. But for those willing to interact with the wallflowers, they can be somewhat fearful of approaching someone with such a standoffish attitude, so it becomes a self-fulfilling feedback cycle.
Even just a little courage can go a long way. Walking across an open space can make you more approachable; for example, walking from somewhere on the edge of an activity like a dance to wherever beverages are being served can give others an opportunity to intercept you or approach you. It's not hard, it just takes some practice and the realization that the possibilities for negative consequences are much lower than the possibilities for positive outcomes.
Honestly, that may be the case for some, but I suspect that the majority of the time it's much simpler: Afraid to be in a small-talk situation, and not know what to say after a couple of words. In short, it's a phobia of the feeling of awkwardness. Easier to avoid.
Like any phobia, the best way to treat it is by exposure -- putting yourself in awkward situations as much as possible and witnessing that you can handle it/ get out of it. But also like any phobia, that's much, much easier said than done.
If I go to a music show or a coffee shop or on a walk it doesn't mean I left my kitchen for the exclusive purpose of finding a dating partner.
Alot of girls actually prefer places where they can be in public and be left alone and not shamed for it or assumed to be advertising themselves, or otherwise prone to mental disease or emotional inadequacies because they don't want to socialize.
In fact places like bars, gyms and other places where women go for the same reasons men go, to enjoy a stiff drink or get in a good workout, pride and advertise themselves for being safe havens with no tolerance for making women feel like they are out of place for existing alone outside of the home.
Not wanting to be approached doesn't mean not wanting to observe others interactions at the event.
Using military terminology is kind of brutally honest, yet clarifies the situation, if I've been trying to run a stealthy recon mission to observe intel to prep for possible later missions (or not...), a sudden sneak attack by an outnumbering flanking welcome wagon force is can be panic inducing, defensive fire and run for emergency evac.
More prosaic its like walking into a new store trying to soak up the vibe and feel of the theme and product lines and style and other customers, then getting pounced on by a salesdroid demanding full attention so they can close a sale to me on whatever gives them the best commission, not cool man, that's why internet shopping is crushing brick and mortar.
That's plain false, and quite frankly a mean assessment. Being somewhere by yourself and not interacting can be a choice and can make for an enjoyable time out. Your broad-sweeping statement is unfounded and offensive.
As a wallflower I wish people would start conversations with socially inept people like me and help them ease in public outings
As someone who has to fight my natural introversion I've noticed it is very hard to talk to someone who is literally standing by a wall. There's no way to approach them except deliberately, and.. well why would anyone try talking to someone who is hard to talk to when there are easier options.
Instead, have a plan. And your plan includes at least one conversation map, which gets you through at least 2 minutes of conversation.
Feel free to steal mine: Go and get a drink (it doesn't have to be alcoholic) and then say this to the person next to you:
"Excuse me, I'm XXX. Do you know anyone here?". Their answer is either "Yes.. this is YYYY". Then you go "Hi! What do you do?". Or else they go "No, I don't know anyone either." Then you go: "Oh, I hate coming to this kind of thing when I don't know anyone. So what do you do?"
The next level of this is to bring a third person in. Wait until you see someone looking lost (remember, you are near the food/drink, so people are walking past you) and go "Hi, I'm XXXX and this is YYYY. YYYY is a blah blah blah", and now you know at least 2 people, and are at the core of a group of people talking.
(Ultimately there has to be a reason they are at a social gathering; if it's not because somebody else made them go, then they want to socialize).
There's the fear of not being able to keep going with smalltalk and such, but also the conflicting desire for interaction.