I mean, he's really not part of the story. There's a reason he's not in the film trilogy. Nothing wrong with that but he really is a side quest or whatever you want to call it.
"Old knives are long enough as swords for hobbit-people," he said. "Sharp blades are good to have, if Shire-folk go walking, east, south, or far away into dark and danger." Then he told them that these blades were forged many long years ago by Men of Westernesse: they were foes of the Dark Lord, but they were overcome by the evil king of Carn Dûm in the Land of Angmar.
"Few now remember them," Tom murmured...
https://tolkiengateway.net/wiki/Letter_144
But I don't really disagree with your comment in general.
Moreover, his removal dismisses and reduces the work of the unnamed smith who wrought the blade of Westernesse whose work came to fruition in its small part in the undoing of the Witch King of Angmar to a mere clattering of cutlery on a bed in a Bree.
A better way to handle it would've been a fade to black as the Hobbits pass into The Old Forest, and their then awaking on a hill w/ swords menacingly arrayed around them (across their neck would be a bit much w/o someone to actively remove them), some jewelry glittering on a nearby stump, their ponies neatly tied up nearby, and a song fading off into the distance as a man in bright blue jacket, leather pants, yellow boots, and a hat w/ a feather in it rode into the Old Forest.