  We explore the whole phase space of the so called Veneziano/QCD ghost dark
energy models where the dynamics of the inner trapping horizon is ignored and
also the more realistic models where the time-dependence of the horizon is
taken into consideration. We pay special attention to the choice of phase space
variables leading to bounded and compact phase space so that no critical point
of physical interest is missing. It is demonstrated that ghost dark energy is
not a suitable candidate to explain the presently accepted cosmological
paradigm since no critical point associated with matter dominance is found in
the physical phase space of the model. A transient stage of matter dominance --
responsible for the observed amount of cosmic structure -- is an essential
ingredient of the accepted cosmological paradigm. The above drawback is in
addition to the well known problem with classical instability against small
perturbations of the background density originated from negativity of the sound
speed squared.
