It’s up to the owners to change the rules for reinstatement. Giamatti left that door open. He made the decision most favorable to Rose that he could without ignoring the evidence or the rules.
I’ll admit I’m a bit fuzzy on Hall of Fame vs. eligibility to compete in a game.
They need to separate eligibility to work in baseball from eligibility for the Hall of Fame.
But the same permanent ineligibility is keeping Joe Jackson out. (Arguably Buck Weaver as well, though Jackson’s case for the Hall of Fame is clearer than Weaver’s.)
The Hall decided after the first time Rose came up for vote (and got basically no votes) that banned players were banned from the Hall. Honestly it probably save him the embarrassment of getting voted against over and over until running out of his eligibility. But the ban was lifetime, so in theory he’s eligible now.