Now that Major League Baseball commissioner Rob Manfred has removed Pete Rose, “Shoeless” Joe Jackson and other deceased players from the game’s “permanently ineligible list,” whatever former stars deemed deserving based on their on-field accomplishments should, at first opportunity, be inducted into the Hall of Fame.

In a bombshell, if long overdue, reversal of policy, first reported by ESPN’s Don Van Natta Jr. on Tuesday, Manfred removed bans for Rose (who bet on games while managing the Cincinnati Reds) and members of the 1919 Chicago White Sox (who fixed the World Series), among others.

After all, banishment was meaningless once they all had died -- a life sentence, if you will, for whatever their transgression. Most died decades ago and were on the list for gambling-related offenses.

“Obviously, a person no longer with us cannot represent a threat to the integrity of the game,” Manfred wrote in a letter to the attorney who petitioned for Rose.

The only remaining purpose of the ban was to keep them from the immortality of being inducted into Cooperstown, which bills itself officially as the “National Baseball Hall of Fame and Museum.”

The last word is the most important.

Should Rose and the others have done what they did? Of course not. Should they have been subject to any potential criminal or civil recourse for their actions? Absolutely. Was MLB within its rights to suspend or punish them in other ways? Definitely.

Rose, for example, should never have been allowed to work in baseball again after it was determined he bet on the Reds to win games while he was the manager.

But that doesn’t mean his record 4,256 hits, his three World Series titles, his MVP award (1973), his 17 All-Star appearances (including when he barreled over catcher Ray Fosse in the 1970 game), his “Charlie Hustle” nickname, or that epic head-first slide shown so many times on “This Week in Baseball” that a generation of kids either crushed their chests or chipped their teeth trying to emulate it -- didn’t occur.

It’s about a nice day in central New York State with your family, complete with a gift shop.

If the museum is there to tell the history of the sport, well, how do you do it without Pete Rose? If Hall of Fame induction is reserved for the greatest players, then how could Rose not be among them? His foolishness as a manager shouldn’t have eclipsed his impact as a player.

This is where baseball’s policy was always wrong. It used the prospect of barred entry to the Hall as a deterrence. That isn’t what a museum should be about. The risk of criminal charges, lost wages from suspension and general shame should be enough. If it isn’t, so be it.

Manfred isn’t ready to release those still living from the ineligible list. He’s clinging to the concept of scaring current players straight. “It is hard to conceive of a penalty that has more deterrent effect than one that lasts a lifetime with no reprieve,” he wrote in the letter.

In fairness, their personal failings didn’t affect baseball the way Rose might have as a managerial gambler, and certainly not as the Black Sox did back in the day.

Still, there are owners and commissioners in the Hall who worked for decades to stop baseball from racial integration. That’s a far more widespread impact on the integrity of the game than betting on your team to beat the Dodgers.

History is history. The game is the game. The museum is the museum. Tell the story, the whole story, with all the best players and best teams and best tales, no matter how colorful, criminal or regrettable.

America can handle it.