[Inziladun]

'Power' beyond one's native abilities is not generally well-considered in these works. Yes, the intentions of the makers of the Three, and those who wielded them, were good. Yes, they were somewhat successful in their desires to preserve the past. But, as you say, this was not in line with the doom, or fate intended for them. They used power that did not belong to them to make a semblance of deathlessness. And again, that was not natural to the state of things in Middle-earth: it was a hollow echo of the true immortality of the Undying Lands, and someone like Galadriel, who had experienced the real thing, would have perceived that. I don't think she ever intended for Lórien to be permanent. In fact, a section of the chapter devoted to her and Celeborn in UT says she advised that the Three should be hidden and never used, after the loss of the One. She longed to return to the West, but believed herself still in exile. She lived in a carefully constructed fantasy of the Undying Lands, hoping against hope she could one day return there. Her statement that she wished the One had remained lost can be explained by her having regret that the party had to end so soon, and in such a fashion: because it had been found, she knew that one way or the other she would finally lose all she had gained by the use of Nenya.
This has no textual basis I am aware of, but to me it would seem the ultimate cheat of Doom if any Elves living under the shadow of an artifact of power created by themselves would have been allowed to use it for eternity, or near it, and keep themselves in guarded 'museums' while Ilúvatar's plan for the return of the Elves to Valinor and the start of the Dominion of Men in Middle-earth took a back seat. Would that really have been possible?