He's not a freaking Kryptonian pretending to be human! He's a human being who happens to have alien physiology. Changes that put this other stuff into the Superman 'stream of consciousness' diminish the character rather than boost him.
***
Being an immigrant myself, I have something of an insight, I think, into the way Clark's mind works. I was born in England, and I am proud of my English heritage (I was also quite a lot older than Kal-El when I left "home", so my connections would be stronger) but I grew up in Canada and I have lived for the last 25 years in the US, and I don't ever -- ever -- feel like a "displaced Englishman".
Clark would be proud, too, of his Kryptonian heritage, but later portrayals of him have tried to shoehorn in too much of the pychobabble of adopted children longing for and seeking out their biological parents. Excuse my French, but to me, they fall under the heading of "ungrateful little sh*ts".
Clark grew up as human, thinks as a human, reacts as a human. He lives and loves as a human. And that is what really defines him.