It provides some pretty key context to where Merry got his blade from and why it is able to break the spell and make the Witch King killable. Bit of a better explanation than Eowyn's "I am no man."
"Fear not, Macbeth; no man that's born of woman. Shall e'er have power upon thee."
In Macbeth that turns out to be a man who was a Caesarean birth but Tolkein thought that was a cheap solution to the problem. A hobbit and a woman, now we're talking.
And if you think about that you realize the ents and huorn were a reference too:
"[he] shall never vanquished be until the Great Birnam Wood to high Dunsinane Hill shall come against him"
It turns out that Tolkein confirmed that the huorn and the ents came from his disappointment as a child that the trees in Macbeth were just guys wearing branches.
Once you know that it's hard to look at the books in the same way. You have to compare Denethor's role as unfaithful steward with the stewards in Macbeth and pretty soon you're just running a comparative literature class in your head.
Who's Wormtongue supposed to be? Is he a reference to King Lear's daughters? Is the scene where he tries to marry Eowyn a reference to Richard III?
Aragorn's speech is awfully Henry V, and the return of the Army of the Dead is awfully like the WWI short-story of the Angels of Mons where Henry's army returned to the aid of the British line.
Searching for tropes is a normal part of reading literature but normally you're just looking for parallels. I wish he hadn't included an actual reference to Macbeth to force the issue.
I always thought it was more of a misleading prophecy, very like Macbeth (probably inspired by? Tolkien certainly drew some inspiration from Macbeth in other areas); "No man of woman born" and "Not by the hand of man" are both interpreted as "can't be killed" but really turn out to have very significant loopholes.
The origin of the blade is relevant because they nearly died in getting it, and because it came from the tomb of a prince who himself died battling the Witch King, so in a sense he obtained vengeance from beyond the grave. "Wow, this sword just turned out to be magic, what a coincidence" isn't nearly the same thing.
The films also had to deal with the fact that the LoTR books had a lot of material after the ring was destroyed--and that's not even counting all the material in the appendix of RoTK. Say whatever positive things you like about LoTR but the narrative structure of RoTK in particular is a bit of a mess.
That doesn't mean movies are better: in fact, movies are clearly more limited and worse, from the point of view of telling long, complicated stories. But people enjoy movies (me too), so... compromises.
Reading had a massive renaissance with gen z and millennials have always read more than boomers.
The idea that the youth consider reading as geeky and boring is itself and outdated idea from the 80’s.