In early Chinese history, minting of coins was at times quite decentralized. These were interspersed with attempts at centralization, enforced with brutal measures.
I have a recent response on early Chinese understanding of inflation and deflation here that I'll steal from/build off of.
By the time of the Warring States, when different coins had emerged in different states, minting of coins appears to differed between states. In the more centralized peripheral powers, such as Qin or Chu, there were huge mints in the capitals, and evidentially punishments for private minting. Variable quality of coins in Qin suggest that there may have been either illicit private minting or less than ideal control at state run mints, and unlike weapons, coins weren't stamped with their foundry to guarantee quality. In the more decentralized states of the central plains, minting was scattered throughout the state, and we find evidence of it near privately run weapons workshops. Interestingly, they minted all types of coins, including the round Qin coins and coins found in Chu, and not just local coins. These would have presumably been used for private interstate commerce, and speak to the connectedness of the Chinese world at the time.
Once Qin unified China, the First Emperor seems to have made an attempt at unifying coins, at least coins being minted. However, this process was disrupted by the rapid collapse of Qin following his death. The resulting wars further disrupted the production of coins. Furthermore, when the Han was finally founded, it wasn't initially a unified state that Qin was. During its establishment Emperor Gaozu established several vassal states under control of allies, top generals (who mostly ended up later liquidated by his empress), and relatives. Presumably to both ameliorate the coinage shortage, and as a concession to these states, private minting of coins was allowed. This did create more coins, but also led to inflation and low quality coins being circulated.
There was some opposition to private minting at this time, the poet and essayist Jia Yi opposed private minting on three grounds. First, it was impossible to enforce consistent standards, and private coins were repeatedly diluted with lead or iron. Secondly, the coinage situation in early Han was very chaotic, with coins differing between localities as small as counties, private minting made this situation even worse. Finally, being able to mint their own coins diverted labor from agriculture, which was by far the most important of all economic activity. His solution was somewhat different though: instead of directly monopolizing minting, the government should monopolize copper mines, providing copper only to trusted private mints. As far as I know it was never attempted.
After Emperor Gaozu's death, Empress Dowager Lü seized control of the empire. Excavated fragments of laws issued under her suggest she attempted to recentralize the economy and minting of coins, issuing a new heavier coin. Yet the coin was too heavy and was rapidly melted down for its base metal, and she was unable to stamp out private minting, leading to her issuing a new lighter coin. Following her death, coinage was once again allowed to be minted privately by the less interventionist Emperor Wen. He brought imperial supervision to private minting, requiring private mints to register with the government, meet standards to avoid the hilariously light coins private mints churned out during the reign of the Han's founder, and pay a fee to the government for the right to mint coins. This seems to have been quite successful, stabilizing the currency and, while not eliminating shoddily made coins, at least reducing the scope for abuse.
The next Emperor, Jing, saw yet another reversal in the policy of minting coins. While continuing the general noninterventionism of his father Emperor Wen, he crushed a group of rebellious vassal states led by imperial princes in the rebellion of the seven states. In the aftermath of the rebellion, he also abolished private minting of coins, making it a capital offense. It would generally remain a capital offense during periods where private minting was illegal.
Under his successor, Emperor Wu, a much larger centralization of the economy would occur. This was postponed by the influence of his grandmother, Grand Empress Dowager Dou. She would greatly influence the less interventionist stances of the previous two emperors, and while alive, thwarted Wu in his attempts at centralization, but failed in having him removed. After she died he was free to move ahead. Various monopolies were established, most famously in salt and iron, but also goods like wine. The brilliant official Sang Hongyang implemented a price equalization scheme quite similar to that outlined in Guan Zi, where the government would buy goods when they are cheap and sell them when they are expensive, making a ton money and smoothing prices in the market.
More directly relevant for this question is, a reasonably successful attempt at standardizing coinage across China was carried out. He first expanded government mints throughout the country, but it proved impossible to control for quality of their coins. He also tried various interesting experiments, such as the introduction of a fiat deer hide bill, that all failed. Finally, a new central mint in the capital was created. This produced an absolutely massive amount of coins each year, up to 400 million coins, backed by tens of thousands of convict slave laborers in mines, forges, and mints. This was enforced through widespread arrests, sentences of forced labor, and executions, though it could have been worse, as many, perhaps up to a million people, were pardoned in various empire wide pardons of grace.
