It has been the conventional wisdom in nuclear physics since the 1960s that a unified theory of nuclear structure is impossible. However, already in 1937 Eugene Wigner indicated a way forward in theoretical work that eventually led to a Nobel Prize, but not directly to unification. Specifically, he showed that the symmetries of the Schrodinger equation have an intrinsic face-centered-cubic (FCC) geometry. Those symmetries provide for a fully quantum mechanical integration of the diverse models of nuclear structure theory, as indicated by the following facts: (i) The FCC lattice reproduces the properties of the liquid-drop model due to short-range nucleon-nucleon interactions (constant core density, saturation of binding energies, nuclear radii dependent on the number of nucleons, vibrational states, etc.). (ii) There is an inherent tetrahedral subgrouping of nucleons in the close-packed lattice (producing configurations of alpha clusters identical to those in the cluster models). And, most importantly, (iii) all of the quantum n-shells, and j- and m-subshells of the independent-particle model are reproduced as spherical, cylindrical and conical substructures within the FCC lattice -- with, moreover, proton and neutron occupancies in each shell and subshell identical to those known from the shell model. These facts were established in the 1970s and 1980s, but the "impossibility of unification" had already achieved the status of dogma by the 1960s. Here, I present the case for viewing the lattice model as a unification of traditional nuclear structure theory -- an unambiguous example of how declarations of the "impossibility" of progress can impede progress.