We can't prove he effected the outcome of games to win them. There is no prove he bet against his team.
If Rose was only betting on his team to win, then obviously - it logically must follow - the days he did not place a bet on his team is a bet against. A bet is a statement of confidence - no bet, no confidence.
And again, speaking of logical conclusions - as manager, Rose decides who plays and who doesn't. If Rose has 5,000 riding on Reds vs. Astros, suppose he uses his best reliever for a third straight night when that reliever needs the night off, just in the hope that he can cover his bet? That taints the game and could jeopardize the health of that player or any player he rides too hard in the interests of covering his bets. That's just wrong.
We can allow all sort of bad people in the HOF, but we can't allow a gambler in even though he may be the best player to ever play the game. Gambling is something millions of people do each day.
Do you know why people gamble on sporting events? They gamble on the assumption that they are watching something honest. If those people in 1987 who laid down hard-earned money on the Reds knew the manager of the team did not place a bet on his team on one night or other, do you think they would do the same? Let's say Joe Torre gambled on games, present day. If I knew next season that Joe Torre didn't bet on the Dodgers vs. Brewers, July 11th, I would also not place a bet to that effect. Because I know that Torre believes his team won't get it done that night, and that he will not push as hard for a win when he didn't place a bet.
Did Player X beating his wife or Player Y's racism effect the outcome of baseball games? Highly unlikely. Did Pete Rose, playing certain players on certain days and withholding certain players on other days, effect the outcome of baseball games? Most likely. And he wasn't doing that for the good of the Reds, he was doing it for his own personal gain. Putting his goals ahead of the team.
Pete Rose is not banned from baseball because he gambled. Pete Rose is banned because he broke the rule against gambling.