: Bombadil has a tremendous impact on the story. Merry cannot kill the Witch-king without him

::snip

Merry needed the knife from the Barrow-downs to kill the Witch-King. Bombadil was crucial in his obtaining it.

But are we to suppose that the knives in the Barrow were the only ones the Men of Arthedain ever made to slay their enemy, the King of Angmar? If I were them, I'd have made as many as I could, within reason anyway.

I think that, had the hobbits not met Bombadil nor gone to the Barrow-downs, they could have encountered the same sort of weapons elsewhere. One likely possibility is Rivendell's armory.

::snip
: Pippin and Merry cannot bond with Treebeard without him

I have no idea what you are talking about here. What role did Bombadil have in the relationship between the hobbits and Treebeard?

: Frodo isn't prepared to accept the journey over Sea without him, etc. Bombadil is felt throughout the story, right up until the very end.

I don't know what you're talking about here, either, unless it is in reference to some of the dreams that Frodo had under Bombadil's roof.

I like Tom as a character, and an anachronism. But if you take away Tom and the Barrow-downs, and the restriction on what weapons can harm the Witch-King, and the story works just the same.