Elves: truly immortal?

[Reginald Hill]

I know that many times in LotR Tolkien refers to man's mortality as the "doom of man," but did he not also say

for the longvity of the Quendi was derived primarily from their fëar, whose nature or 'doom' was to abide in Arda until its end.

It seems worse to live forever (the elves must tire of the world sometime). Just like that book Tuck, Everlasting, didn't the immortal family advise the kid not to drink form the fountain (that might be wrong, because I read the book a long time ago, but I think they didn't want to live forever).
This raises the interesting question of whether it is better to live "forever" or to go to ME "heaven" faster.