  The dressed-metric approach is shown to violate general covariance by
demonstrating that it cannot have an off-shell completion in which the correct
infinitesimal relations of space-time hypersurface deformations are realized.
The main underlying reason -- a separation of background degrees of freedom and
modes of inhomogeneity that is incompatible with covariance -- is shared with
other approaches such as hybrid loop quantum cosmology.
