The problem with that idea is that it would never actually all get destroyed. The Russians, the Chinese, the Koreans (and the DoD probably as well) would just say “sure we destroyed ours” but they would never actually do it. None of the major players would risk unilateral disarmament.
Well, there are only two highly controlled stocks - and the Russian’s play far better these days than they used to, so unlikely that any would be hidden. Thank G*d the Chinese don’t have fingers in this pie...