Smoothing over structures in general relativity leads to a renormalization of the background and potentially many other effects which are poorly understood. Observables such as the distance–redshift relation when averaged on the sky do not necessarily yield the same smooth model which arises when performing spatial averages. These issues are thought to be of technical interest only in the standard model of cosmology, giving only tiny corrections. However, when we try to calculate observable quantities such as the all-sky average of the distance–redshift relation, we find that perturbation theory delivers divergent answers in the UV and corrections to the background of order unity. There are further problems. Second-order perturbations are the same size as first-order ones, and fourth-order at least the same as second, and possibly much larger, owing to the divergences. Much hinges on a coincidental balance of two numbers: the primordial power and the ratio between the comoving Hubble scales at matter-radiation equality and today. Consequently, it is far from obvious that backreaction is irrelevant even in the concordance model, however natural it intuitively seems.