MLB's chief baseball officer Joe Torre explained the decision Sunday.
"Just a uniformity that we try to bring to all the teams," Torre said, according to Danny Abriano of SNY. "If we allow one team - somebody, God forbid, a young child - and you wind up able to do stuff everywhere. That's the only issue. In order to be uniform and be fair to all the other teams, we try to keep the game hats on for the games."
Torre added that the policy is unlikely to change.
After the league denied the request, Alonso and the Mets donned custom cleats honoring 9/11 first responders without asking MLB's permission, though the league elected not to fine or discipline the team.
Torre said he understands why players want to pay tribute, but suggested it's a slippery slope if the league makes exceptions.
"We try to keep the hats the way they are because every team could really have a legitimate reason to want to wear a different hat to honor something that happened in their particular area," he said.
Regarding 9/11, Torre added, "There's no question that's something you never want to forget and is something that - you don't celebrate it, you commemorate it. I understand that. But again, probably you have New Yorkers living and playing for other teams too that can't do it that would like to do it."
Torre did say that the league could potentially adopt a special uniform for the "memory of 9/11," but it would need to be for all teams and not just one.