Having read the book and not seen the movie, I object to calling Arwen “boring and insipid”. Maybe this is Peter Jackson's Arwen, but it is definitely not Tolkien's.
In the Lord of the Rings book, Arwen is only here as Aragorn's love interest. This isn't completely gratuitous on Aragorn: it shows his close relationship (indeed, his alliance) with Elves, in an age when elves are mostly withdrawn from the Human world. But it is true that Arwen is not a well-developed character. Arwen gets little mention, and only through Frodo's eyes. This is for good reason: The Lord of the Rings is not her story.
It is commonly cited as one of the most major differences between the book and Peter Jackson's movies that Arwen gets more airtime in the movies, without being a more fleshed-out character.
Arwen and Aragorn's story is told in Appendix A.V of The Lord of the Rings. There is more to her than what can transpire in the main story. When Aragorn first meets her, he reacts thus:
Then Aragorn was abashed, for he saw the elven-light in her eyes and the wisdom of many days; yet from that hour he loved Arwen Undómiel daughter of Elrond.
An important fact about Arwen, which I think is only mentioned in the Appendix, is why Arwen becomes mortal. This is unrelated to the Ring. Arwen is the daughter of the half-Elf Elrond, and the mortality of Elf/Human hybrids is a bit quirky. As Elrond puts it:
"What is that doom?" said Aragorn.
"That so long as I abide here, she shall live with the youth of the Eldar," answered Elrond, "and when I depart, she shall go with me, if she so chooses."
Elrond's immortality was granted by the Valar, and it is not unconditionally transmitted to his children. At the end of The Lord of the Rings, all the Elves left in Middle-earth leave for the West. If Arwen remains behind, then she no longer benefits from the boon of immortality granted to her by association with Elrond. As the magic leaves Middle-earth, her Human side takes over, and she becomes mortal.
Thus by marrying Aragorn, Arwen makes the choice of mortality. She has literally chosen to live and die for Aragorn. It is therefore not surprising that she would no longer wish to live once Aragorn is dead.
On top of that, two lovers who cannot be long parted and die together or nearly so is a trope (Together in death? That's not exactly it, but it's the same idea).
A further matter of importance is that Arwen and Aragorn's love story is the modern echo of an older, very important legend: that of Lúthien and Beren, the ur-mixed-couple. There are multiple allusions to Lúthien and Beren's story in The Lord of the Rings (starting with the ballad sung by Aragorn in chapter I.11). The story of Lúthien and Beren is one of the most important in the Middle-Earth universe. It is told in The Silmarillion (and in other posthumously published material). Arwen, Aragorn and their entourage are aware that that they are repeating history.
In a long letter (131 in the Letters of J.R.R. Tolkien) to Milton Waldman (who worked for the publishers of LotR) in 1951, Tolkien wrote:
But the highest love-story, that of Aragorn and Arwen Elrond's daughter is only alluded to as a known thing. It is told elsewhere in a short tale, Of Aragorn and Arwen Undómiel. I think the simple 'rustic' love of Sam and his Rosie (nowhere elaborated) is absolutely essential to the study of his (the chief hero's) character, and to the theme of the relation of ordinary life (breathing, eating, working, begetting) and quests, sacrifice, causes, and the 'longing for Elves', and sheer beauty.
And in a 1954 letter to Peter Hastings (153):
Arwen is not a 're-incarnation' of Lúthien (that in the view of this mythical history would be impossible, since Lúthien has died like a mortal and left the world of time) but a descendant very like her in looks, character, and fate. When she weds Aragorn (whose love-story elsewhere recounted is not here central and only occasionally referred to) she 'makes
the choice of Lúthien', so the grief at her parting from Elrond is specially poignant.
Also, in a never-sent draft (181):
Here I am only concerned with Death as part of the nature, physical and spiritual, of Man, and with Hope without guarantees. That is why I regard the tale of Arwen and Aragorn as the most important of the Appendices; it is part of the essential story, and is only placed so, because it could not be worked into the main narrative without destroying its structure: which is planned to be 'hobbito-centric', that is, primarily a study of the ennoblement (or sanctification) of the humble.
Tolkien highlights that Arwen perceived Frodo's unease after having been (albeit briefly) possessed by the Ring, which others including Gandalf had missed. (LotR VI.6; letter 246 quoted below):
I do not myself see that the breaking of [Frodo's] mind and will under demonic pressure after torment was any more a moral failure than the breaking of his body would have been – say, by being strangled by Gollum, or crushed by a falling rock.
That appears to have been the judgement of Gandalf and Aragorn and of
all who learned the full story of his journey. Certainly nothing would be
concealed by Frodo! But what Frodo himself felt about the events is quite
He appears at first to have had no sense of guilt (III 224-5); he was
restored to sanity and peace. But then he thought that he had given his
life in sacrifice: he expected to die very soon. But he did not, and one
can observe the disquiet growing in him. Arwen was the first to observe the
signs, and gave him her jewel for comfort, and thought of a way of healing
Humphrey Carpenter and Christopher Tolkien note what this “way of healing him” is: she is largely to thank for Frodo being able to sail West! As far as I know, this is never stated in The Lord of the Rings or any other non-posthumous material.
What is meant is that it was Arwen who first thought of sending Frodo into the West, and put in a plea for him to Gandalf (direct or through Galadriel, or both), and she used her own renunciation of the right to go West as an argument. Her renunciation and suffering were related to and enmeshed with Frodo's: both were parts of a plan for the regeneration of the state of Men. Her prayer might therefore be specially effective, and her plan have a certain equity of exchange.