I agree. I was there at the time (although only 8 years old). From '56 through '64 certainly, My Fair Lady was considered the greatest Broadway musical ever, not to be fucked with, if and when filmed.
I just wish they had chosen Minnelli over Cukor as the director. Cukor had never solely directed a "book musical" film. Regarding One Hour with You, the great Lubitsch replaced Cukor, although George continued as his assistant. In A Star Is Born and Les Girls, the songs were all musical numbers, performed diegetically.