We know from LotR that:
- The Children of Elrond all had the choice to be counted among either Men or Elves.
- That this Choice needed to be made at the time when Elrond would leave for Valinor - they could either sail with Elrond and remain immortal or stay behind as mortals.
- That because of this stipulation, Arwen needed to make a choice between immortality and marrying Aragorn, since she could not stay behind and retain immortality. And given that both her brothers remained behind, they both seem to have chosen mortality as well.
So it strikes me that the entire heartache, at least when it came to Arwen (since we do not know why Elladan and Elrohir chose as they did) could have been easily avoided by Elrond staying on Middle-Earth until the end of Aragorn's life, which would be a mere 100-150 years at most, thus postponing his Children's Choice and allowing Arwen, at least, to have her cake and eat it too.
So, is there any reason given by Tolkien in any of writings on why Elrond needed to leave at that exact point, and couldn't have stayed on for just a century more? We know that Celeborn, Galadriel's husband and Elrond's father-in-law stayed on in Rivendell for many years into the Fourth Age, so it doesn't seem to be purely about being a Elf.
Is there anything from Tolkien that answers this question?