Why did Rose throw the diamond necklace overboard?

In Titanic, the elderly Rose visits a ship searching for the Heart of the Ocean diamond, set in a necklace. Unbeknownst to them, she actually carries it with her.

In one of the final scenes, a bare footed Rose walks to the railing of the search ship, climbs up on it in similar fashion to when she and Jack were on the prow of the Titanic, and throws it into the ocean.

The accepted answer in Why did Lovett invite Rose aboard his search boat in Titanic? suggests Rose threw it overboard for 'closure', but I simply cannot understand how that was closure. After all, it is not as though Jack (when alive) had any real interest in it. Nor did Rose. It was of interest only to her fiance Cal (who took his own life in 1929, when the stock market crashed).

It could be said that the return of the 'Heart of the Ocean' to the ocean, was ..poetic in a sense, but how was it closure? If not closure, then why did she do it?

Update

Interestingly, the original script differs from the movie in that the people searching for the diamond are there to witness her throwing it overboard. She even has a few words with Lovett as he is holding the object of his desire in his hand.

You look for treasure in the wrong place, Mr. Lovett. Only life is precious, and making each day count.

Another snatch of the script that might be relevant:

The hardest part of being so poor, was being so rich. But every time I thought of selling it, I thought of Cal. And somehow I always got by without his help.