We show that the canonical oscillation-based (non-resonant) production of sterile neutrino dark matter is inconsistent at $>99$% confidence with observations of galaxies in the Local Group. We set lower limits on the non-resonant sterile neutrino mass of $2.5$ keV (equivalent to $0.7$ keV thermal mass) using phase-space densities derived for dwarf satellite galaxies of the Milky Way, as well as limits of $8.8$ keV (equivalent to $1.8$ keV thermal mass) based on subhalo counts of $N$-body simulations of M 31 analogues. Combined with improved upper mass limits derived from significantly deeper X-ray data of M 31 with full consideration for background variations, we show that there remains little room for non-resonant production if sterile neutrinos are to explain $100$% of the dark matter abundance. Resonant and non-oscillation sterile neutrino production remain viable mechanisms for generating sufficient dark matter sterile neutrinos.