One of the many reasons i love ouran is the way it handles the concepts of change and personal growth. As we can see, in the beginning each character deals with their own inner struggles. For Kyoya it's extremely high expectations his family sets for him and inability to express himself the way he wants to. For the twins it's the fact that they want people to see them as two separate individuals. For Haruhi it's her fear of getting too attached to other people and losing control over her life, thus missing out on life. Hani wants to be a good leader for his clan, but doesn't want to pretend to be someone he's not.
When Tamaki invites them to join the host club, he sees that they all have flaws and that they all are, despite trying to put up a tough front, just children who want to be loved and understood. I think that he sees himself in them as he was robbed of love and desperately craved it too. So he didn't just pick random handsome boys for his club, i think he was looking for "lost boys", who needed home.
And despite Tamaki being mostly shown as careless and naive person, he's very perceptive and wise. The way he can read others is absolutely phenomenal to me (that's what he and Haruhi have in common). And what i find especially heartwarming, that despite all of them being reluctant to join the host club, pushing Tamaki away, most of the time being harsh and rude to him, he still accepts them the way they are. Because he sees that they have potential to change and become better, to figure themselves out and blossom into something exceptionally beautiful.
And i love how the characters don't change overnight, it takes time for them to come to terms with the fact that they actually want to change, which is very realistic, in my opinion. Because no matter how many people are trying to help you and lead you towards the right path, unless you make an effort, no change will happen.
The characters don't immediately stop being stuck up rich kids, who make questionable choices and mistakes, they learn as they go and gradually become better people. And Tamaki is there to support them each step of the way, because he genuinely cares about these dorks and sees them as his family.
And even though the show makes fun of his "family issues" and him thinking of himself as the "dad" of the group, I honestly think that it's not so far from the truth. He's like a father figure to all of them in some sense, he helps them to understand themselves and the world around them. He's being patient and supportive like a truly good parent that wants the best for his children. I think that it's a very wholesome concept of a found family.
And I'm happy that Tamaki was right about them, because all of them have turned out amazing in the end.