Now, as far as whether or not it is ever cool to keep rings like those and regift them... let me give you an example:
My ex-fiance proposed to me with a $5900 designer Ritani ring. It has almost two carats, but Ritani does not certify them, for whatever reason. It's an amazing ring, set in platinum, and I really loved it. The downside came when he tried to sell it (once we had split up and I have given it back). The most he could get for it was a little under $1K.
That's a ridiculous loss to take on such a huge investment. I TOLD him he should have it reset into a pendant or some other such piece to give to his sister or his mother, or maybe even a future girlfriend.
There's nothing wrong with that.