If we consider the Elven rings to be a creation similar to the Silmarils, a nice parallel arises.
FŽanor attempts to "capture" or enhance the exquisite beauty native to Arda. This act, while a tribute like unto AulŽ's, is still a vain attempt at stamping one's mark on the Creation. It is willful, flying too close to the sun - literally, the fire of the Jewels burns as would the daystar.
The magic rings, likewise, are at first a pure craft which sustains and heals and enhances the glory of Arda. But again, there is the desire to somehow control and "own," as well as heal, the material world.
This desire is fostered in the Elves. The shadow enters their hearts, their culture. Therefore, they effectively create the snare that binds them. It is an ancient lesson: the most effective weapon to be used against you, will be the one you make. Sauron embodies this lesson. From an objective view, the Elves destroy themselves. Of course, they get rid of the Rings when they realize what has happened; we do notice, however, that Sauron exists "roughly" the same amount of time that the last of the Elven rings exist.
Carl Jung describes the Shadow, the darkest aspect of our Self or Ego, as the most easily accessed and simultaneously the most difficult to overcome. Because the Shadow is carried, from war to war, ring to ring, there is never any true escape - save death only.
Whatever we do, whatever we make, the moment we love it too much or are unable to cast away the "treasure" at need - that is the appointment of the hour of our Doom.