Pete Rose was sanctioned by baseball, and he accepted the lifetime suspension. The steroid guys never had the book thrown at them by MLB.
So, Rose cannot be on the ballot while alive, but the PED-users can. It is up to the HoF voters to decide if they should be in given their drug use.
As for betting, Rose claimed bet on his own team, and not against it, but he did not bet on the team every game. That would affect his management of the team, and potentially the outcome of more than a single game.
Respectfully, your logic is circular. Baseball could lift his lifetime suspension at any time. If Rose played for the Boston Red Sox or the New York Yankees, he would’ve been enshrined 20 years ago.