Barkis, I think the argument has been pretty convincingly made that yes, betting on baseball is uniquely harmful in ways that the other transgressions you mention are not. You may feel that drunkenness and drug smuggling are worse moral failings than gambling, but the point is not that Pete Rose did morally bad things, but that he* broke the rules of baseball.* AFAIK, baseball does not have rules against playing drunk or smuggling drugs (and Cepeda was retired when he did that, anyway; it probably did delay his HoF induction by several years). I am quite sure that if such rules do exist, they leave more leeway to the Commissioner than the rule against gambling, which flatly states “shall be declared permanently ineligible”.
The Ty Cobb stuff is interesting, but you will note that the article you linked to says that the rule Rose was banned for breaking was instituted AFTER the Cobb scandal, so you can’t claim that Rose is being treated unfairly based on the relatively lenient treatment afforded Cobb.
In any case, I can’t imagine any scenario in which I would advocate throwing anyone OUT of the Hall of Fame. The damage that would be done to the institution by creating that precedent, so that fans would fear that their favorite player might be de-inducted decades after the fact, would far outweigh the damage done by letting in some reprobates. I oppose putting Rose in the Hall of Fame, but if he should ever be inducted, that will end the argument forever as far as I’m concerned.