In a nutshell: ontology is the concern of theologians, not of philosophers who are interested in its prior, knowledge. Most of what remains of ancient Greek has been transmitted by theologically minded authors. Thus the illusion is created that ontology is somehow a fundamental philosophical question. It was Kant who rejected the theologian's view and separated again the concerns. "Existence is not a real predicate" (KRV) became the cornerstone of modern philosophy. Since Descartes it was obvious that subject comes first and everything else follows.
Fragments of Parmenides that has been preserved do not really prove any importance of ontological questions. Lebedev has forcefully argued that an incorrect reading allowed the realist interpretation of thinking and being is the same:
Zeller's... reading eliminates «idealism» from Parmendides’ text and
turns it into a positivist platitude, namely that the object of
thought must be something real.Zeller’ interpretation was accepted by
Burnet in EGPh and through his influence has become widely accepted in
the English-speaking literature on Parmenides. The ancient
interpretation, however, hasbeen defended and retained by Diels-Kranz,
Mario Untersteiner,Gregory Vlastos, Charles Kahn, Marcel Conche, Ernst
Heitsch,Cordero among others. Zeller’s interpretation is grammatically
(Lebedev, A. 2017: Parmenides ΑΝΗΡ ΠΥΘΑΓΟΡΕΙΟΣ. Monistic
Idealism (Mentalism) in Archaic Greek Metaphysics, online)-
Even without Nietzsche it is clear that the theologians' claim for power and authority rests upon an ontological position. Philosophers do not have such pretensions and history shows just how their craft was co-opted as the servant of theology.