Thermoelectric materials, enabling direct waste-heat to electricity conversion, need to be highly electrically conducting while simultaneously thermally insulating. This is fundamentally challenging since electrical and thermal conduction usually change in tandem. In quasi-two-dimensional conjugated coordination polymer films we discover a new advantageous thermoelectric transport regime, in which charge transport is defect-tolerant but heat propagation is defect-sensitive; it imparts the ideal mix of antithetical properties – temperature-activated, exceptionally low lattice thermal conductivities of 0.2 W m-1 K-1 below Kittel's limit originating from small-amplitude, quasi-harmonic lattice dynamics with disorder-limited lifetimes and vibrational scattering length on the order of interatomic spacing, and high electrical conductivities up to 2000 S cm-1 with metallic temperature dependence, notably in poorly crystalline structures with paracrystallinity > 10%. These materials offer attractive properties, such as ease of processing and defect tolerance, for applications, that require fast charge, but slow heat transport. The database contains the DFT-optimized structure of Cu3-BHT with 60 atoms in the primitive cell.