He does not necessarily "play" young, though. And I always thought Harrison rather on the old side for Higgins. Ian Richardson, who did the 1976 revival, was about right, and he was much nearer to Benedict in age than to Rex. And he is, after all, an actor. And he isn't playing Father Christmas.
I think most (if not all) of the Eliza candidates mentioned in this thread are too old. To my mind, the ideal Eliza would be under 25. I think youthfulness is an important trait in Eliza. I also hope they cast a lesser known actress in the role (mainly because I can't think of any "name" performers that young who could play it). If they want to cast a star, they can get one for Higgins.
This is a different take on My Fair Lady. This clip doesn't do justice to the production. I've seen the production which is a joy from beginning to end.