The Hall of Fame is a separate entity to MLB. Writers for the most part do the determining of who gets the nod for entry. Pete for his on field accomplishments would be automatic. His ban by MLB for gambling doesn’t preclude his entry but writers think its a factor enough to keep him out for now. As time goes by that may change but also maybe not. Shoeless Joe still ain’t in.
It has nothing to do with the writers. The Hall Of Fame and MLB are separate entities, but the HOF bylaws stipulate that a person banned from MLB is ineligible for admission.