Let him in. Never bet against his own team. If you bet on your own team so what? Who does it hurt?
Your stud reliever has worked three straight games and really needs a day off. But you've got 50K on today's game and you're leading 5-3. Unlike most games that you simply want to win, you NEED to win this one because you've got 50K on it and you're already in debt 100K to your bookie. So you pitch your exhausted reliever, whose mechanics are messed up and he blows out his elbow and he's done for the year and his career might never be the same.
Substitute the stud starter for the above scenario. He has worked 8 tough innings and he's tired but your bullpen blows. It's just some June game so, if you didn't have money on it you would just go to the bullpen and take your chances. But you have 50K on it so you HAVE to win. So you roll the dice that your starter can give you one more inning.
Substitute an extra-innings scenario where a reliever has worked 6 innings and you have no pitchers left. If you didn't have 50K on the game, you might do what countless managers before you have done and throw a shortstop or outfielder on the mound. But you've got 50K on it so you make the pitcher work another inning.
Those are just three examples. I could give others. Betting on your team not an acceptable excuse.
Back in my writing days, my "solution" to the Rose situation was this:
He never was accused of better as a player, and so he should be eligible to go into the Hall as a player; let the BBWAA use its discretion to vote on him, just as its members have the discretion to vote on juicers. Meanwhile, because he was a steward of the game as a manager and he knowingly and brazenly broke the rules, he should be forever barred from having anything to do with baseball: he can't serve as a manager, GM, consultant, broadcaster, ambassador, etc.
What in fact has happened is that baseball has gone the other way: They've let him back into the game in some minor ambassador-type roles and apparently now as an announcer. Which means they've let a guy who broke Rule No. 1 as a steward of the game become a representative of the sport he disrespected. But they won't let him be considered to have a plaque in a museum.
Having said all that, if Rose is never let in the Hall, it wouldn't bother me one iota. He didn't make a "mistake," he knowingly violated baseball's oldest and most stringent rule and then lied about it for more than a decade.