Benedict wasn't inducted in the first dozen classes.
(After 11 other goalies. It wasn't until 1966.)
Why not?
The Hockey Hall of Fame was and still is to some extent an "old boys club."
Benedict ruffled a lot of people's feathers throughout his playing career that seemed to have an effect on his Hall of Fame status. Stats-wise and looking at his career, he should have been inducted within the first five years of the Hockey Hall of Fame existing. However, for one, Benedict had problems with alcohol that led to Ottawa getting rid of him at the height of his career. He was able to resurrect his career with the Maroons and won another Stanley Cup, but the damage was done.
This is not confirmed either by any means (and honestly how can it), but his family members have rumoured to me that he had gotten in trouble with an under-aged girl during his career and it was quietly swept under the rug and wasn't in the press.
Personality-wise, he was also very abrasive, a "my way or the highway" type of guy, that you can see with the whole falling down on his knees to make saves when it was still illegal and eventually having the rule changed.
Benedict was finally inducted in 1966, I believe, after a couple of people on the selection committee had passed away, who were keeping him out over the years.