I'm not sure I can since the question is mostly a subjective one. But, I don't think he should be in the Hall of Fame since he was not "the guy" in his division at any point during his career.
I suppose you could argue that someone need not be "the champ" in cases where he was avoided and did not ever get a championship fight. I also think you could just have one of the titles and not the lineal title too. But, you have to be the guy at some point in any division where you have fought. He had the opportunity to be the guy but fell short. So, he falls short of the Hall too.
I don't mean this to be a slight on the career of Carl. I just have a different standard for entering the Hall than some.
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