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.

I'm ok with him being omitted from the film, but I'm glad the novel could afford more space for someone like him, a foil to the mood of impending doom, and also just plain fun. He rescued them and equipped them, and one of the weapons he supplied played a pivotal role later. Merry would not have been successful without that blade, and Tom is a believable source for such immense help. There's a book of Tolkien's letters and in letter 144 he explicitly says he intended Tom to be an enigma because he felt there should be some in the mythical age of the story.

"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

https://tolkiengateway.net/wiki/Letter_153

https://tolkienessays.com/tom.html

He marks the transition between the world of _The Hobbit_ and that of the new world without magic which _The Lord of the Ring_ presages --- c.f., Lord Dunsany's _The Charwoman's Shadow_ which JRRT certainly had in the back of his mind as the manuscript grew from "Hobbit Sequel" (w/ a Hobbit named "Trotter" as the first iteration of the Ranger named "Strider" whose name in Eldar is not so ill, _Telcontar_).

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.