A QUESTION OF FAITH AND VANITY via The Lord of the Rings

I don't have as many audio books as I'd like; however the books I do have are excellent, and that counts for something.  I'm back to The Lord of the Rings on the rotation, and I heard, or came near understanding, something yesterday afternoon I haven't before.

Context: The fellowship is just ending their stay at Lothlorien, and Galadriel  is speaking to Frodo of the necessary elvish departure of Middle Earth--all elves preparing or already en route.  Their destination is the Gray Havens and they are prepared and intend to never return--at least as far as I understand it (my LoR lore is not quite full-geek).

Galadriel's claim is that the elves must depart Middle Earth, else remain relegated to "caves and dells to be forgotten" (not sure the quotation is exact--sorry), insinuating, in essence, that a departure will be a rescue of sorts, and maintain and even enforce their potency and immortality.  But why do the elves have to leave--and for the "Havens" (Haven = heaven; departure for heaven = death and immortal glory, right)?  Is it because of the ignominy of diminished power, for at the End when the One Ring is destroyed, the other rings of power--Galadriel's Nenya and Elrond's Vilya (I'm pretty sure of those names) --will fade and eventually end (though no one is sure this will happen).  Is their departure a vanity, that they might not fade like their rings, for if they depart--if they quit while they're ahead, as it were--they will yet survive eternally in Middle Earth, if not bodily then in song and lore, where their power will not just linger but grow continually and expand with the hyperbole of time and storytelling?

But if this is indeed it, then it could also be more than this:  Is their departure also an act of faith against the survival of the One Ring--faith that Frodo will succeed, which success, once again, will spell the end of their special gifts of wisdom and power--faith, because if Frodo fails, then there is no precise reason to leave already, if at all, and maybe yet linger in a last ditch attempt to defeat Sauron?  There is, after all, power deliverable by faith, as sure as light travels on waves through the void to Earth (okay, that was pretty cheesy--sorry).  Do they expect--or at least hope--that this demonstration of faith by departure, and even early departure, will act in benefit of the quest?  If so, does the good of this demonstration of enacted faith supersede the vanity of their self-preservation?

I don't know.  This was while driving home from work.