Guys are approaching girls less and less for a variety of reasons. I can give plenty of reasons based on each scenario.
Guys won't approach at a bar unless it's for a one night stand.
Guys won't approach at a gym because it will seem like he just likes her in a physical sense and/or the girl would be uncomfortable being sweaty and all.
Guys won't approach during school because she may be too wrapped up in a book or on the way to another class leaving no time to talk.
The main issue is that there is an approach being made with absolutely no information about the other person and going by no other notion than her physical appearance.
My main reason I haven't struck up a conversation with a girl in a long time: She's always taken. It gets tiring to go through conversation after conversation with someone just to find out she's taken. Plus, many girls don't like admitting they're single. Many girls are insecure about it and feel like there is something wrong with them for being single. So it's not like I can just go up to a random girl and ask "Hey are you single?" I would imagine that being very awkward.
Also think about being with someone, do you want to be constantly getting approached when taken? So the guy is gonna have to hope that the girl don't have an angry boyfriend who gets jealous easily. Lots of girls for whatever reason stay with controlling and aggressive boyfriends which can make for some very hostile issues should her girl get hit on.
Honestly it's better off for the girl to do approaching these days. More and more guys are getting fed up with approaching girls just to find out they're never interested.
I generally approach first just because I don't like the guessing games that go on with trying to wait for "just the right moment." But I approach simply because I'm the one willing to do it sooner. I have been approached by girls before, and the one time that it turned into a relationship was one of the best ones I've ever been in. Girls that purposefully wait give me the impression of a trophy waiting to be won and I don't want a trophy, I want a girlfriend.
Here's the thing though. Guys can still be chivalrous and have the girl approach first. I love being chivalrous. It makes me feel like I am doing relationships right. But something I cannot stand is a girl that demands chivalry. Chivalry is a choice made by the guy, not demanded by a girl. And if it is demanded, it means nothing. If a girl demands chivalry from me, even my mother telling me how I should act, I stop talking to her right then and there and leave. It is something I cannot abide.
All of this being said, it's the 21st century. I hate to bring the sexism into it but here it is. Women want to be equal with men, so pull your weight. Put some effort into life and a relationship, don't just sit there and wait for the man to do all of it for you.
So I guess the main point of this whole rant is, yes. Purposefully waiting for a guy to approach is out of fashion. If you like the guy just go talk to him, make a move.
A lot of younger guys do not approach girls, except for the really cocky and confident types. I think most young men these days have less confidence than they used to in general, which does affect their ability to approach girls. Also, some girls have decided they don't want to wait, so they are taking the bull by the horns and trying to be more proactive. One method isn't better than the other, as long as you get the desired result. If not, a girl should consider switching things up.
In our age of instant communication through social media/cell phones I think less of the approaching is done in person but it still happens a lot.
For your case, being shy and a "wall flower" is always going to hurt your chances of being approached. Guys will approach girls they feel comfortable approaching. If they don't know you or don't think you are "feeling them" they probably won't approach. Just acting a bit more open and friendly can do wonders
Expecting guys to do it 100% of the time, even if you yourself would like to talk to him, is old fashioned. I'm not one for rituals or social rules or anything else like that, but it's unreasonable to not put any effort into connecting with the opposite sex. I don't know if it's been drilled into your head that women don't do that, but regardless I don't think it's healthy to be directly/indirectly teaching girls to be overly shy or passive.
Girls are generally attracted to jerks. Most guys are not jerks. Why would a nice guy willingly set himself up for the pain of rejection?