I'd want to see final cluster quality, not just inertia, before treating "one-tenth the epochs" as a drop-in win. On badly imbalanced or overlapping clusters, Lloyd's often spends early iterations bouncing centroids around. If the interpolation mainly damps that motion, you can look converged on the objective while the partition is still poor. A plot of ARI or NMI versus epoch budget on messy data would make the claim a lot more convincing.