Honestly, that feels extreme. I never thought about it at the time back when I read LotR, but man, that feels wrong.
After all, humans have been dealing with this for as long as they've existed - whether outliving your parents (expected), outliving your spouse and friends (always possible), outliving your children (tragic), or even at the lowest end of that scale, outliving your pets (expected and tragic), outliving your loved ones is just something that will happen.
Tolkien deciding the elf side of a couple always dies of heartbreak because he dislikes the notion of the elf moving on and remarrying that much is kind of rubbish of Tolkien.
If parting is inevitable, then you want the other side to be happy that they were with you for as long as that was possible, and to keep being happy after you're gone.