I'd say any succesful and lasting Hellenic Empire is pretty much going to be a Persian Empire. Persepolis would be the political center.
I don't see why. No ancient empire in the region set up their capital at Persepolis after the Achaemenids-the Seleucids had there's in Syria and Mesopotamia, the Parthians in Ctesiphon, and the native Persian Sassanians in Ctesiphon. The likely seat of power is going to be in either Syria, Kilikia (due to it being at a vital crossroads) or Mesopotamia.
Yeah but you forget the starting point for Alexander's conquests - it was to destroy the Persian empire.
The stated goal of his conquests was to return the greek speaking regions under Achaemenid control to independence. After that it became destroy the Persian empire. In actuality, Alexander's goal from the very beginning was to essentially become king of the Persian Empire, not destroy it.
There were roads in Persia, and the Achaemenids ruled more or less the same territory from Mesopotamia just fine. There can always be two capitals too.
But there's no reason for it to be the capital. It wasn't the capital for the Seleucids, Parthians, or even Persian Sassanians. Even for the Achaemenids it quickly just became one of a few capitals (at first the others being Susa, Ekbatana, and Babylon, but after several Babylonian revolts, the others being Susa and Ekbatana only). Furthermore, any greek empire is always going to be more western oriented than east, by nature of where they get their troops from and just by nature of that being where most of the greek members of the empire lived. It wouldn't make sense to have a capital as far east as Persepolis when Mesopotamia and Syria would do fine. Especially when we consider the Hellenistic rulers had a tendency to found their own capital cities and start from scratch rather than use existing cities as their capitals even when prestigious ones existed (see Seleucids in Mesopotamia).