Why do Elves remain in Middle-earth?

Question

Once there are ships that can take them to the Undying Lands, what is the motivation for the Elves to stay in a war-torn, darkened land full of Men and Orcs and other undesirable creatures? We know that Elves could become wraiths if they stayed in Middle-earth, so something would have to be of value to them enough to outweigh that risk. Their purpose as the Firstborn was to show Men the way and prepare Middle-earth for them, but many of them are not doing that. So what then are they doing?

What's keeping them there?

Sailing into the West seems like an all around better deal for them and I can't find any discussion of a motive to stay.

Answer 1

This is addressed in Tolkien's Letter 131:

There was nothing wrong essentially in their lingering against counsel, still sadly with the mortal lands of their old heroic deeds. But they wanted to have their cake without eating it. They wanted the peace and bliss and perfect memory of 'The West', and yet to remain on the ordinary earth where their prestige as the highest people, above wild Elves, dwarves, and Men, was greater than at the bottom of the hierarchy of Valinor.

In other words, in Middle-earth the Elves are the highest, the most revered, the most powerful. In Valinor: they're not.

Note that there are exceptions. The Avari, who never left Middle-earth in the first place, obviously have little motivation to go West. On the other hand the likes of Galadriel, who - at the time of The Lord of the Rings - was the sole survivor of the rebellion of the Noldor, were under a ban from returning and therefore had no choice in the matter. Letter 297 elaborates:

The Exiles were allowed to return — save for a few chief actors in the rebellion of whom at the time of the L. R. only Galadriel remained.

Answer 2

In The Silmarillion, at the end of the "Of the Voyage of Eärendil and the War of Wrath" it is said:

"Yet not all the Eldalië were willing to forsake the Hither Lands, where they had long suffered and long dwelt; and some lingered many an age in Middle-earth. Among those were Círdan the shipwright and Celeborn of Doriath, with Galadriel his wife, who alone remained of those who led the Noldor to exile in Beleriand."

That said, someone else may correct me, but I have never seen anywhere that the purpose of the elves is "...to show Men the way and prepare Middle-earth for them, but many of them are not doing that so what then are they doing, what's keeping them there?"

The Valar didn't even all agree on bringing them to Valinor in the first place, as is said in The Silmarillion ("Of the Coming of the Elves and the Captivity of Melkor"):

For some, and of those Ulmo was the chief, held that the Quendi should be left free to walk as they would in Middle-earth and with their gift of skill to order all the lands and heal their hurts.

Their purpose in Arda is to be elves and live and enjoy Arda, the same as men and Ainur, each race with its own way. Also, note that most men in Middle-earth have never been in contact with elves, men from the east and from Harad. And from those lands, those who have been in contact with elves, have been mostly through war.