It seems to me the audience is with Eliza from the get go. Everyone sees Higgins as an imperious, misogynistic baby, including his mother. The songs are clearly satirical (Why Can't a Woman be More like a Man? and A Hymn to Him) and is behavior is abusive and unthinking. Why do you think Eliza has a number about how she wants to see him executed? She does learn, but then rebels. No one would ever adopt his methods either in 1910, 1956 or today. The crucial moment in the musical is when Higgins beautifully describes the glory of the English language. His compassion and vision is the key to Eliza actually learning and we witness the moment (The Rain In Spain). It's one of the few moments when we see there may be more to Higgins than his bullying.
