They had to get a singing Tyrone Power

"...But Faye needed a singing leading man and Power great actor that he was, was not it".

Yes, John Payne filled that bill.....somewhat. The son of professional singers, his voice was much too studied for my tastes, although his baritone was rich enough. His best singing, with Alice, was in "The Great American Broadcast," which also features GREAT performances from "The Ink Spots" and "The Nicholas Brothers." This film is not highly rated, but the songs and the dancing numbers make it an under-appreciated classic. Alice was obviously limited in her choice of partners while working at 20th Penitentiary-Fox (as she called it), so any duets with, say, Bing Crosby were out of the question, in that she couldn't even sign a record deal and all of her singing was limited to films only. In that their voices were actually of equal range (Alice was practically a tenor), the combination of Crosby and Faye would have been a delight.

Nobody cared if Tyrone Power could sing. He was a handsome leading man and Fox's biggest star and Fox would put him anywhere they thought would boost their box office. He worked well with Alice Faye in Old Chicago and they were re-teamed. I think it was one of his best movies and I understand it was a huge hit in its time.

John Payne was good. I saw him recently in "Garden of the Moon" (made about the same time as "Alexander") and he was good (and attractive) but he never made the impact Tyrone did on the public no matter what Fox did for him.
He made some good movies with Betty Grable and some passable westerns in later years.