Quantum chemical high-throughput screenings of compound libraries for the identifications of materials with the desired properties have emerged as beneficial tools to accelerate the discoveries of compounds of interest. The quantum chemical high-throughput screenings of compound libraries require the definitions of reliable descriptors enabling relationships between the observed physical properties and the computed electronic structures. The desire to enhance the discoveries of materials showing electronic instabilities which are related to possible metal-to-superconductor transitions stimulated our impetus to probe the feasibility of a descriptor for the identifications of materials with the aforementioned electronic instabilities in the forms of flat bands crossing the Fermi levels. To evaluate the reliability of the projected descriptor based on the flat band/steep band scenario for superconductors, we inspected the characteristics of the electronic band structures near the Fermi levels for a series of chalcogenide superconductors, whose electronic structures were computed and analyzed by means of first-principles-based high-throughput techniques.