If Rose had been an LA native, and had the same career with the Dodgers, he would be totally despised by Reds fans, but the Rose cult in LA would be even bigger than it is in Cincinnati today.
If he had played for the Yankees, and been born in NYC, he would have never been caught betting on the game, and would today be in the HoF. There are too many people there who would have helped him, in any way possible.
Rose has not been the only player to bet on baseball since 1920 (no, I have no proof of this; these things don't happen in a vacuum, however). No way, no how. He was the only one dumb enough to be caught, however.