Honestly you don't even need the secret identity in place to use the duality, it just draws a clear line between the two that's easier for people to write around without having to think too hard about it. The lack of the ID could even fuel a lot of really great stories as Clark learns, for the first time in his life, how to live a single life instead of two.
That's the trap I think DC falls into a lot with this; the secret identity exists because of the duality, not the other way around. There was no duality in post-Crisis when the ID was still secret ("Clark is who I am..."), there's no duality now that it's public. And that's wrong. The duality exists regardless of whether people know who Clark is or not. That's the way Clark has lived his entire life, it's not a consequence of his being Superman it was there from the start; the moment young Clark realized that not everyone could see and hear and do the things he can, the dual existence was born.
Some writer, I think it might've been Yang, said that the true character is found in the tension between Clark and Superman. The secret identity helps to visualize and compartmentalize that for readers (and short-sighted writers), but this goes deeper than just whether people know who Clark is or not; this is how the man experiences his entire life.