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Q: How accurate is it?

A: It is accurate to describe most societies up to late antiquity as command economies.

The term command economy is abstracted here to mean the converse of a market economy where market forces drive economic action. In other words an economy where a ruler gives orders and others obey (with some nuance—more in that in a second). By and large societies in antiquity were command economies as rulers claimed what little agricultural surplus was generated by their kingdoms to supply their artisans (including armorers and tool and weapon makers), priests, merchants, and administrators, whose numbers were minuscule compared to the vast majority of the populace. Military innovations spread slowly and gradually, and highly disruptive practices such as charioteers (requiring such skilled workers as wheelwrights and bowyers) resulted in new aristocracies of mounted warriors overthrowing the old rulers, substituting one command system for another. And the skilled labor always remained under the control of the ruler, simply because it did not take many to create a stock of arms that could be used for more than one campaign and to replenish materiel losses during that campaign.

Q: So to what degree was central planning possible?

A: There tended to be an optimal size to these polities that restricted the administrative reach of the ruler, driven by the tax and rent systems set up to immunize the subsistence farmers from plunder. Where you see some influence of market forces is through the control of strategic commodities, requiring rulers to negotiate or seize sources of valuable metals, for instance. During Xerxes’s invasion of Greece, he strayed well beyond what was considered to be a 90 day radius of action from Persepolis, his administrative center and place of muster, and taking into account his agents stockpiling foodstuffs along the way rather than allowing an army on the move to strip the countryside of its agricultural wealth. In fact it was his central planning that allowed a Persian army to operate for as long as it did in a land as resource poor as Greece. Strategic blunders and delays allowed the allied Greek city-states to fortify the Isthmus of Corinth, which the Persian army did not have time to campaign against before they ran out of food, leaving naval resupply as the only option; the Battle of Salamis put a swift end to that option, leaving the Persian army the choices of withdrawal or starvation.

So why not have more than one capital to extend your RoA? Supporting an administrative center of that nature again requires a surplus classical societies did not have, and there are many instances of rulers delegating power to leaders on the fringe who then become vassals in name only. In both Persia and China outlying garrisons were modest compared to the power that could be brought to bear from a centrally located capital, to prevent fomenting rebellion or secession.

Q: How was it achieved?

A: As with diplomacy through the ages—bargaining, persuasion, punishment, threats, gifts, military action. Humans are probably biologically predisposed to a command environment because it is the first type of relationship we become aware of: parents command and children obey (or not, but with consequences).

Source: The Pursuit of Power, W. McNeill. EDIT additional source: my mental notes of a Military History class I took in college taught by Prof Sumida, who did his PhD under McNeill.

EDIT: forgot about Egypt. The various necropolises should provide the evidence for the degree of central planning possible under the non-Hellenic rule of Egypt. It took 20 years worth of agricultural surplus to construct a pyramid, an undertaking possible only with skilled labor which generally did not result in economic benefit to the populace. The New Kingdom benefited from having a standing professional corps of charioteers ensuring dominance for generations.