I hear what you're saying, and I don't believe he cheated in any way.
However, the rule - and the precedent - was absolutely clear. Doesn't really matter if it was fair, that's what the rule was.
As noted above, Joe Jackson was banned for life after taking money from a gambler. The fact that Joe went on to be blisteringly hot during the series, showing that there was no way he was doing what the gamblers wanted, did not save him. Baseball decided that the integrity of the game cannot be called into question by association with gambling. Period. Jackson is not in the Hall even now, despite continuing campaigns based on the fact that he obviously was outright cheating the gamblers - took their money, then thumbed his nose at them.
Even if it was unfair that Rose be banned for betting FOR his team, the fact is that he bet. He knew the rule, and he knew he was headed for the Hall if he kept his nose clean. He took a risk, and got caught.
If you do the crime, you better know you may do the time.