Yeah. It is. Women don't approach the vast majority of men, and they definitely don't drop the handkerchief. Relationships just don't happen if men can't approach women, and women deliberately put themselves into harems with the small minority of men they do actually chase. Nobody wins.
If you keep doing approaches out of the blue, especially in the setting the manga depicted, they definitely won't happen, no matter how much you insist. And of course, that will be the only experience you'll ever know: classic selection bias.
Relationships still happen to everyone else (and no, it's not a minority of people), and they don't require chasing, they require proper social settings, like shared venues (hobbies, classes, volunteering, social events), for example, where you show that you are an approachable person and you treat your peers as human beings, regardless of who they are. If you are willing to meet this low bar, you'll have people crushing on you and asking you out, no manipulation required. It does require socializing and to not fuck-zoning people though, and too many men find that challenging, especially the latter.
Also, do you seriously think there are women that put themselves into harems like so many mangas show? Really?