This is the real reason they had to steal the egg "twice":
If you recall in a black & white flashback, when Danny and Rusty are holding a secret meeting with Gaspar LeMarc, LeMarc says,
"you will have to assume that the moment this challenge begins, Toulour will have you under constant surveillance. You will have to put on an elaborate show..."
Later in the movie they show the second part of the meeting where LeMarc tells them where the real egg is. So, in order to fake out Toulour, they had to "act" out one plan to steal the Egg from the museum, and hold that "act" all the way through until the very end.
If Toulour caught on that they had a different plan and knew where the real egg was, he could've found a way to beat them to the real egg or steal it from Ocean's 11 after they got it. So they had to be 100% convincing in their act all the way through the end stealing the fake egg. This is proven by Toulour and Danny meeting at the end of the movie at Toulour's house where Toulour believes he has won, Ocean's 11 failed, and the "whole crew got pinched." This is further proven by Toulour saying that Tess looks nothing like Julia Roberts, and their plan was never going to work.
Toulour clearly knew every step of their "fake" plan from surveilling them, which they acted out all the way until the very end. Toulour finally realizes he was conned, duped, and that Danny had to have talked to LeMarc to have the real egg, and he lost. This is proven again during an exchange between Rusty and Isabel, where Rusty says Toulour is the best, but he's going to lose. She seems confused. How can you win if you can't beat him and he's better. Rusty knows, it's because of leMarc telling them where the real egg is and Toulour will be stealing a fake. Danny and Rusty admit throughout the movie Toulour can't be beat. So they knew, in NO WAY they could give away that they knew where the real egg was. They had to act out the second heist of the egg to ensure they had the real egg safe.
Why did LeMarc tell Danny & Rusty about the real egg, and not Toulour, his protégé? Because Rusty had one more piece of leverage, LeMarc's daughter, Isabel Lahiri (Catherine Zeta Jones).. Isabel's mother (LeMarc's wife), made Lemarc swear to leave and stay out of Isabel's life forever, or she would turn him in. So he never got to see his daughter since she was a child.
Rusty dated Isabel, and now has met with LeMarc, and Rusty knew that if he could promise LeMarc he could unite him and his daughter Isabel, Le Marc would help them with the challenge and they would win for sure. Lemarc says, "and i'm still getting the better of you two" to Rusty and Danny, because he's getting the real egg at no expense or risk of his own, AND his daughter back, all for just telling them where the real egg is.
There it is!