The DSHARP survey evidenced the ubiquity of substructure in the mm dust distribution of large, bright protoplanetary discs. Intriguingly, these datasets have yet higher resolution information that is not recovered in a CLEAN image. We first show that the intrinsic performance of the CLEAN algorithm is resolution-limited. Then analyzing all 20 DSHARP sources using the 1D, super-resolution code Frankenstein (frank), we accurately fit the 1D visibilities to a mean factor of 4.3 longer baseline than the Fourier transform of the CLEAN images and a factor of 3.0 longer baseline than the transform of the CLEAN component models. This yields a higher resolution brightness profile for each source, identifying new substructure interior to 30 au in multiple discs; resolving known gaps to be deeper, wider, and more structured; and known rings to be narrower and brighter. Across the survey, high contrast gaps are an average 14% wider and 44% deeper in the frank profiles relative to CLEAN, and high contrast rings are an average 26% narrower. Categorizing the frank brightness profiles into trends, we find that the relative scarcity of features interior to 30 au in the survey's CLEAN images is an artifact of resolving power, rather than an intrinsic rarity of inner disc (or compact disc) substructure. Finally the rings in the frank profiles are narrower than the previously inferred deconvolved widths, indicating smaller alpha / St ratios in the local gas disc.