In a depletion region after negative (majority) charge has diffused from n to p, there are not many charge carriers left (electrons have left and holes have been filled), so the material in the depletion region is a poor conductor.
(Another way of thinking about it: remember from E&M that a perfect conductor must have zero electric field inside it, as charges will rearrange themselves to cancel any field. After diffusion, the n-type side has an excess of positive charge, and the p-type side has an excess of negative charge. There is then an electric field across the region from positive to negative, pointing from the n-type to the p-type; only a poor conductor can support an electric field.)
Outside of the depletion region, there are still charge carriers around to conduct current.