I suppose that everybody wants to be somebody.
Sometimes, I think that people are just desperate and are looking for ways to say, "Notice me. I'm unique." But 4 letters doesn't make one anymore special than a zip code makes a town special. What makes a town special and unique from all other towns, even those in the same region with similar culture, are the characters living there. In the same way, what makes a person special is truly knowing herself (or himself) and being comfortable in his or her own skin, so to speak. it's the individual character, not the personality call letters.
So, whether my four letters read ESTJ or INFJ or INTJ or WARP, it doesn't change the essence of who I am and eventually, if I run my mouth long enough, the person I'm talking to is going to form his or her own opinion of me, anyway. It's not my responsibility to confirm or deny that opinion, but only to remain true to my own character. Still, the call letters are simply a beginning place on the journey to self-discovery. Many people will find that their initial typing was faulty, not just those who believe themselves to be INFJs.
I wouldn't say that everyone wants to be INFJ. I would say that many people have at least some reason to believe they are.
So, for example, if I discovered tomorrow or in the next five minutes that one in every three people had my identical cognitive functions preference, it really wouldn't make any difference, because I'd still be the only me and it would just mean there were a lot of AWESOME people in the world! (Just kidding. I'm not really that arrogant, but I do like myself and I don't see any point in lying about it!)