Also what I did. It's really the only logical assumption!

I found that too. I read these as a child, and I remember siding with those elves who thought Illuvatars Gift to Men to be a hard one to accept. Still, I tried to understand it a gift and not a curse, at last in later years, thinking that there must be something to it, when some elves chose to become mortal and receive this gift.

When I thought of the elves perspective, I can see that while they are super cool, they can't live the lives the way we of mankind do. We have the ability to appreciate life and feel life very intensely, precisely because we know with certainty an upper bound to our expiration date.

(For full disclosure I lean more towards the afterlife being a reality than not, this has of course affected how I read Tolkien, and C.S. Lewis, for that matter...)