There is a very prevalent misconception that Vedic culture favors “monarchy.” We modern people naturally assume this means kings like Henry VIII and so forth, along with their systems of government would be highly approved of by Vedic sages.
This is quite inaccurate.
On this topic, it is very important that we understand the story of Vena, told in the 4th Book of Bhāgavata Purāṇa. The Purāṇa describes the first truly corrupt Monarch in human history (Vena, from which we get our English word for a self-obsessed person: “Vain”). The intellectuals assassinated him (!), and replaced him with an exemplary monarch: Pṛthu.
The book says (at the end of its 18th chapter) that Pṛthu then significantly changed human government. Making it much more elaborate, and giving the citizens built-in means of self-sufficiency and self-protection, fairly autonomous from the Monarch.
For reference, the life of Pṛthu is from the undatable ancient past. So we can say that pure Monarchy existed only before Pṛthu – which was longer ago than we have reliable historical data for.
Extremely early in human (or perhaps super-human) history, people (including monarchs) were naturally good, so there was no need for other social and political arrangements. Once Vena showed that monarchs could be corrupt, Pṛthu saw the need to introduce checks and balances on their power. Thus, throughout most of history, monarchy is an ideal seldom possible to implement without restriction. The modified monarchy introduced by Pṛthu paves the way to our modern forms of government, where the executive leaders are supposed to have relatively little autonomous power.
Vedic culture does not promote Monarchy in any form similar to how we think of it in the West. Even the classical Vedic Monarch is implicitly and explicitly subordinate to the intellectuals who serve as advisors. (A sub-ordinance inherently explicit, as illustrated vividly in the Bhagavatam story by the effortless manner in which the intellectuals disposed of the corrupt monarch, Vena). A Vedic king was never autonomous. He was always a servant of the intellectuals. This is indeed one of the most important pillars of Vedic social theory.
Besides his subordination to the intellectuals, a Vedic Emperor would depute power to regional kings, who in turn would depute power to local mayors, who in turn deputed power to various heads of various boards of affairs. Bhāgavatam credits Pṛthu as the architect of this system. It ensured that people were not absolutely dependent on a single monarch, so that if a monarch died suddenly or became malignant, society had a degree of isolation and protection from the effects, and there would not be an immediate and extreme crisis.
Thus Vedic government is not entirely dissimilar to our modern political theories.