Aerodynamic drag prediction and decomposition into physical constituents is a fundamental research topic, and a clear identification of lift-induced drag in viscous and compressible flows is still an open issue. The recent vortical force theory by Wu et al., based on the Lamb vector field integration, allowed for new induced drag definitions to be proposed for viscous and compressible flows, although inconsistencies were reported in their application, with ambiguities on the physical or non-physical role of a non-zero induced drag found in two-dimensional flows. Domain variations of the drag breakdown in induced and parasite contributions also raised questions on the objective or quasi-objective nature of the two drag concepts. In this paper, classical far-field formulas, thermodynamic-based and Lamb-vector-based drag decompositions are analyzed for both inviscid and viscous flows, at low and high Reynolds number, to clearly identify the conditions for induced drag definitions to provide consistent estimates of the drag due to reversible flow phenomena. A spurious induced drag contribution is otherwise computed, resulting in negative induced drag values in two-dimensional flows. This will be shown to be related to the axial velocity perturbation, while thermodynamic methods will confirm the whole drag being of irreversible nature in all analyzed two-dimensional cases, leaving no space to any non-zero reversible drag.