I think the big problem is betting on a game in which they can decide the outcome. Because if they are allowed to bet... they are also allowed to bet on themselves to lose. I can't think of anything more problematic than that. As far as your Alex Rodriguez argument, you are preaching to the choir. But I go the opposite way. I don't think he, Bonds, Giambi, Palmiero, etc. should be eligible at all. They already stole glory from players like Frank Thomas who was adamantly against steroids and actually tried to start a coups to force for the testing of steroids. I'd argue they also stole money from non-cheaters by signing huge contracts while there was less for honest players.
RE: Should Pete Rose Be Eligible For The MLB Hall Of Fame?