There is a spectacular documentary on him on HBO Max right now. Very insightful.

One detail a lot of people miss: Major League Baseball and the National Baseball Hall of Fame and Museum are not connected at all. National Baseball Hall of Fame and Museum is a private non-profit.

What happened was when MLB announced that Rose agreed to a 'permanent ban' (note the word permanent, not 'lifetime'), the HOF changed their rules and said anyone who is banned from baseball was not eligible to be on the ballot.

The HOF could have any point changed their rule to make him eligible. They could do it tomorrow if they wanted. MLB could also remove his from the permanently ineligible list.