I don't get it -
The Elves just dart off - to leave this world - and let everyone else figure it out.
What private venue to justice or justification of meaning do the Elves have ?
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Because they can.
Imagine you're an elf. You will live forever unless you are killed. Alternatively, you can sail into the West and live in a blissful paradise for all eternity. You would need a very, very good reason to march off to battle and risk a violent death.
Now imagine you have lived in Middle Earth for thousands of years. You have seen many elves die in the wars against Morgoth and Sauron. Meanwhile humans are growing in numbers much faster than the elves ever could. They chop down trees and make the wilderness you love into farmland. Even if Sauron is defeated, in the very long term there is not much place for elves in Middle Earth; and elves have no choice but to look at the very long term.
Under these conditions, the remarkable thing is that some of the elves stayed to fight.
In the past, the elves formed an army to fight Sauron on the battlefield, in the Last Alliance of Elves and Men. By the time of LOTR, they don't have the capability to do that again. They are too few in number and busy protecting their own homes.
In this way, the elves are very similar to the dwarves. Even if they wanted to, they can't gather an army to march off and defend Minas Tirith. The most the elves and dwarves manage is to send Legolas and Gimli as representatives. (I'm referring to the books here; in the films, the elves do send a small army to defend a human kindgom.)
The remaining elves are strong in wisdom and knowledge, not in battle. Elrond and Galadriel use their knowledge to provide invaluable help to Frodo, Aragorn and the rest.