Of course it will not and it cannot be perfect.

When you watch Episode IV Ben says that Vader was his apprentice, and Vader himself calls Ben “master”.
But with some imagination… Ben says that Vader was “a pupil of mine”. It can be seen like “I had many apprentices, Anakin was only one of them”.
And with Vader alling him “master”… well, every Jedi called a higher Jedi “master”.

My purpose is simply to make less obvious that Anakin is Darth Vader… for people who watch it for the first time.
Maybe you want to show the entire saga to your children. If you use another order, you will always have problems with some plot twists or with animated shows like Clone Wars and Rebels, and with spinoffs too.

With this you can watch everything in episodic order.
I, II, Clone Wars, III, Rogue One and so on.
If you really think about it, you start believing that Darth Vader is indeed Anakin, but you can’t be sure.