Indentity and the Fool

I found that I really enjoyed discovering the theme of identity in the play King Lear. I really liked how the fool would often refer to it. It was funny how he baited the king by calling him a fool and saying that Lear'd be a good fool.
But the most interesting part is what was brought up a smidgen in class. Dr. Burton mentioned that Cordelia and the fool aren't ever in the play at the same time. And because of this some people interpret Cordelia and the fool as the same actress.
What I really loved about this idea was that it was so true! The fool was always on King Lear's side, trying to help him fix his problem. But then the fool seems to suddenly and almost mysteriously disappear, never to return to the play. This is only a short time before Cordelia reenters the play and she also is on King Lear's side, trying her hardest to help him out because she actually loves him.
In the end (like all tragedies) Cordelia dies, and King Lear, lamenting, carries her body out and calls her his fool. (Dramatic Pause) Yes, I believe that it is possible that Cordelia actually was the fool. I find her devotion amazing and if she loved her father so much, wouldn't she want to be with him and help him along the whole way? How could a good character like Cordelia just disappear in the middle of the play? I think that she was disguised similarly to Edgar and Kent, seeing as there was a quite large theme of identity going on the whole time.
Just consider it: Cordelia = the fool = Cordelia