What does it mean to be underrepresented in a searchable database? Perhaps the author is making up problems themselves. Or you're wrong. One of the two.
No, gradients can exist in the steady state system depending on the boundary conditions. Additional irregularities can be accounted for by what would ordinarily be considered "discretization error," since the problems considered in the article are discrete structures rather than continuous PDE's.
This is just an occurrence of the principle of least action. Systems exhibiting "hyperuniformity" just arrange themselves in order to minimize their potential. This is pretty standard stuff in engineering, and is the basis for finite element simulations of structural mechanics and fluid dynamics problems.