I think it is perfectly sensible even without Aragorn's backstory.
Explanation:
Marriage between Elves, both because of their steadfast natures and because of their immortality, was intended to last forever.
So Arwen's choice then was this: perpetual missing the person she loved, with no hope of ever loving anyone else, or the great unknown that is mortal death, but with the hope of being able to be with Aragorn.
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