The Barrow-Downs?

[The Might]

Still the initial question remains could LotR have lived without it?
Of course every bit of the story has itw own importance and of course without any part LotR wouldn't be LotR truly any longer, however, I feel that LotR could have lived even without certain scenes, as you can see in the movies.
Don't want to start a big discussion by bringing that up, but the story could have done very well without this passage.
Please do not bring up changes that would have been caused as an argument as that makes no sense.
So what if the Hobbits would have reached Weathertop earlier? Tolkien could easily change it so that they would leave later or make the Nazgul leave earlier or whatever. And the outcome and everything afterwards (still there is the problem with the swords of the Hobbits, but maybe they received them in Rivendell or Tolkien could have thought up something to replace the barrow-wight scene) would have remained the same.
So yes, LotR could have lived without this.