We address a recent extension of the point-particle method to non-dilute clouds dispersed by shock waves and a claim that added mass and viscous unsteady forces remain effective for a significant portion of the transient, "even when the particle-to-gas density ratio is large" (Ling et al, Phys. Fluids, 24, 113301, 2012). We demonstrate that this (Euler-Lagrange) model is prey to numerical instabilities, that the results depend strongly on the method(s) employed to stabilize the computation, and that the claim about the significance of these unsteady forces, for such systems, is unwarranted. Moreover, we show that these problems exist even in the application of this model to dilute dispersions, and that while maintaining the coupling length scales in the calculations yields convergence on grid refinement, the results are not physically meaningful. Further, computations in a fully-Eulerian frameWork, including a multi-field rendition, exhibit fundamentally similar trends, leading us to suggest that the root-cause is to be found in the (common) Eulerian part of the two modeling frameworks. This is confirmed by first-of-a-kind direct numerical simulations, which in agreement with our experiments, reveal that high-speed flows down steep volume-fraction gradients are naturally dispersive. This clearly-stabilizing mechanism is missed in current models; worse, the behaviors they exhibit are cumulative. Based on the detailed DNS results, we present a plan for the way ahead, as we conclude that contrary to many previous "diagnoses", and attempted "remedies", the ill-posedness (name for the catastrophic instabilities discussed) of the mathematical problem is not just an annoying aberration, but rather it is in the very essence of missing these key physics. (C) 2016 Elsevier Ltd. All rights reserved.