  The minimal evolution time between two distinguishable states is of
fundamental interest in quantum physics. Very recently Mirkin et al. argue that
some most common quantum-speed-limit (QSL) bounds which depend on the actual
evolution time do not cleave to the essence of the QSL theory as they grow
indefinitely but the final state is reached at a finite time in a damped
Jaynes-Cummings (JC) model. In this paper, we thoroughly study this puzzling
phenomenon. We find the inconsistent estimates will happen if and only if the
limit of resolution of a calculation program is achieved, through which we
propose that the nature of the inconsistency is not a violation to the essence
of the QSL theory but an illusion caused by the finite precision in numerical
simulations. We also present a generic method to overcome the inconsistent
estimates and confirm its effectiveness in both amplitude-damping and
phase-damping channels. Additionally, we show special cases which may restrict
the QSL bound defined by "quantumness".
