  We discover a "no semistability at infinity" phenomenon for complete
Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance
of an intermediate K-semistable cone in the 2-step degeneration theory
developed by Donaldson and the first author. It is in sharp contrast to the
setting of local singularities of K\"ahler-Einstein metrics. A byproduct of the
proof is a polynomial convergence rate to the asymptotic cone for such
manifolds, which bridges the gap between the general theory of
Colding-Minicozzi and the classification results of Conlon-Hein.
