Neither did Cary Grant, who was the greatest male movie star of all-time, and certainly one of the handsomest.
It could be that the handsomest nominees almost always deliver inferior performances.
c.1400, handsom "easy to handle, ready at hand," from hand (n.) + -some (1). Sense extended to "fair size, considerable" (1570s), then "having fine form, good-looking" (1580s). Meaning "generous" (in handsome reward, etc.) first recorded 1680s.
[Americans] use the word "handsome" much more extensively than we do: saying that Webster made a handsome speech in the Senate: that a lady talks handsomely, (eloquently:) that a book sells handsomely. A gentleman asked me on the Catskill Mountain, whether I thought the sun handsomer there than at New York. [Harriet Martineau, "Society in America," 1837]Related: Handsomeness.
high* wide* and handsome