Recently, Kayyalha et al. (2019 Phys. Rev. Lett. 122 047003) reported on anomalous enhancement of the self-field critical currents, Ic(sf,T), at low temperatures in Nb/BiSbTeSe2-nanoribbon/Nb Josephson junctions. The enhancement was attributed to the low-energy Andreev bound states arising from winding of the electronic wave function around the circumference of the topological insulator BiSbTeSe2 nanoribbon. In this paper, we show that identical enhancement in Ic(sf,T) and in the upper critical field, Bc2(T), at approximately same reduced temperatures, were reported by several research groups in atomically thin junctions based on a variety of Dirac-cone materials (DCM) earlier. Our analysis shows that in all these S/DCM/S systems the enhancement is due to a new superconducting band opening. Taking in account that several intrinsic superconductors also exhibit the effect of new superconducting band(s) opening when sample thickness becomes thinner than the ground state out-of-plane coherence length, we strength our previous proposal that there is a new phenomenon of additional superconducting band(s) opening in atomically thin films.