Imagine letting a Hawk Harrelson vote. His only criteria is if the guy played for the White Sox. Way too many homers in the electronic media.
Hawk is not an electronic media guy. He’s paid by the white sox to broadcast games. No way you could let a person paid by a team to vote, just for the reason you stated..
That said, there are plenty of baseball related guys who’d be better to vote than current baseball writers who aren’t employed by teams.