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We explore the whole phase space of the so called Veneziano/QCD ghost darkenergy models where the dynamics of the inner trapping horizon is ignored andalso the more realistic models where the time-dependence of the horizon istaken into consideration. We pay special attention to the choice of phase spacevariables leading to bounded and compact phase space so that no critical pointof physical interest is missing. It is demonstrated that ghost dark energy isnot a suitable candidate to explain the presently accepted cosmologicalparadigm since no critical point associated with matter dominance is found inthe physical phase space of the model. A transient stage of matter dominance --responsible for the observed amount of cosmic structure -- is an essentialingredient of the accepted cosmological paradigm. The above drawback is inaddition to the well known problem with classical instability against smallperturbations of the background density originated from negativity of the soundspeed squared.

QCD ghost dark energy cannot (even roughly) explain the main features of the accepted cosmological paradigm