Yes, I think he should be reinstated.
Two, I think gambling on a game should be allowed for players, coaches, managers and all personnel involved with that team. One of my caveats is that this is done via a blockchain so that we know their verified wallet. I imagine sports betting companies would love this as they are already paying athletes to promote their product and services.
My reasoning is that radical transparency will always trump radical privacy when it comes to truth and honesty. This works for crypto and I believe it can for sports gambling as well. Money amplifies the character of a person. The game theory implications of this could be fun.
Third, Pete Rose apologized. In my life, I forgive someone who said they are sorry. Do I allow them into my life at a deeper level than they were before? That depends on the person and the situation. In Pete’s case he went the rest of his earthly life without being honored for the hall of fame. A posthumous induction to the hall of fame makes sense in the current spirit of the game.