First off, Grant has stage experience. Secondly, he's tired of being a film actor with all the takes and re-takes. Thirdly, I think he has more depth than his film roles might suggest.
He's the right age for Higgins and certainly LOOKS the part. I'll bet that he can sing it better than Rex Harrison or Jeremy Irons.
No, I stand by my suggestion that Hugh Grant would make an impressive Higgins.
"Long live God!" (GODSPELL)