That illustrates a principle reason why there is insufficient gold to maintain a proper money supply. I love the ring on my hand too. People withdraw gold for too many non-monetary reasons. It is too beloved.
The reality is that gold jewelry is not "withdrawn" from the system but is part of it, just as much as that double eagle.
As inflation increases and savings shrink because the dollars that comprise savings lose value, jewelry begins to be converted back into bullion. Jewelry, especially gold and diamonds are subconsciously, sometimes explicitly, bought in part as a store of wealth.