It's hard to imagine most of the population striving for this and successfully keeping it a secret from outsiders.
Well, secrecy is a key part of the process even in the DS9 take on it. The people in charge of joining lie to everybody about compatibility issues; people who have already been joined may be in on the conspiracy (as our very own Dax was out cold and unable to comment in the episode where the conspiracy was revealed to the other heroes, "Equilibrium").
Just because being a Freemason or a Lion or an Alpha Phi Omegan or a Golden Pheasant or whatever is an advantageous social position doesn't mean that such membership would actually be publicly advertised, or that the society in question be marketed to the general population in any way.
First of all, even in "The Host", Odan wasn't intentionally trying
to keep his true nature a secret.
Second, even if joining were a secret for some reason, it would darn difficult to have large portions of the population applying and trying to be the best and brightest in whatever field they were in and not have outsiders find out.