If Sauron did indeed put some of his power into the foundations of Barad-dur, thay may explain why Elrond and co. did not take the foundations down; quite possibly they couldn't. With some of Sauron's power in them, it may be that, as long as Sauron "lived", the foundations were indescructable.
Another point may be the foundations may have not have been "built" in the sense we are thinking. Going back further, to Melkor's Angbad and Utumno, I have always thought that they might not have been "built" in the sense we think; but putting stone upon stone. Given Melkor's power he may have actually casued both structures to form from the living rock, or have had some of his fire Maiar (like the Balrogs and Dragons, when they were not off battling) melt all of the stones together, so the castle became one solid mass. If he could make volcanos, this could be witin his power. Doing something of this magnitude to the whole of Barad Dur would likely be beyond Saurons strength, but doing it to the foundations might not have been, especially for a powered up early Sauron. If he did, then the foundations would be hard to break.
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