Keep the factors, not the reconstruction
The reconstruction is still dense and the same size as the input. Compressing storage means keeping the factors, not the reconstruction.
U_k, σ_k and Vt_k take k · (H + W · C + 1) scalars, against H · W · C dense — at equal precision.
That count grows with k, so at high rank the factors cost more than the dense data. A factors/dense ratio above 1 means the factors use more scalars than the original.