Though Broadway audiences some years after "Star!" would have been likely more open to seeing Andrews in a sophisticated kind of role than, say, the general movie-going public where she had been playing a role so unlike her two famous movie nanny roles which really made her a movie star. But you're probably right -- something associated with Gertrude Lawrence for a run by then could have been a kind of trigger for Andrews which she wanted to avoid. She later did do a recording of "The King & I"; Anna would have been another wonderful (Gertrude Lawrence) role for her on stage.
