I want to learn more about this from leftist perspective. The neolib standard is that it is better when central bank and the government (finance ministry/treasury) are separate to avoid political and private sector "interference".

Of course we know that the private sector part is especially bullshit considering how much money Federal Reserve or ECB created for the capitalists during the pandemic (or during every other financial crises).

This appears to me as an excuse to not create money for social spending or public services but I do want to read more about it. All the standard neolib sources are such bullshit:

Wiki:

The economic logic behind central bank independence is that when governments delegate monetary policy to an independent central bank (with an anti-inflationary purpose) and away from elected politicians, monetary policy will not reflect the interests of the politicians. When governments control monetary policy, politicians may be tempted to boost economic activity in advance of an election to the detriment of the long-term health of the economy and the country. As a consequence, financial markets may not consider future commitments to low inflation to be credible when monetary policy is in the hands of elected officials, which increases the risk of capital flight.

This basically says Government can't do good things because bad things MAY happen in future. When hasn't capitalism shat itself every decade?

There is very strong consensus among economists that an independent central bank can run a more credible monetary policy, making market expectations more responsive to signals from the central bank.[32]

Neolib source: https://www.igmchicago.org/surveys/fed-appointments/

And a ton of :citations-needed:

Both the Bank of England (1997) and the European Central Bank have been made independent and follow a set of published inflation targets so that markets know what to expect.[citation needed]

Even the People's Bank of China has been accorded great latitude, though in China the official role of the bank remains that of a national bank rather than a central bank, underlined by the official refusal to "unpeg" the yuan or to revalue it "under pressure".

:xigma-male:

The fact that the Communist Party is not elected also relieves the pressure to please people, increasing its independence.[citation needed]

The IMF's Financial Services Action Plan (FSAP) review self-assessment, for example, includes a number of questions about central bank independence in the transparency section. An independent central bank will score higher in the review than one that is not independent.[citation needed]

China protects its markets from foreign speculators. Even Public Sector Commercial Banks in China listen to the party:

https://www.scmp.com/news/china/economy/article/1906325/how-beijing-and-hong-kong-sent-billionaire-george-soros-packing

“When Soros blew the war horn in 1997, many domestic companies and individuals in Thailand or Malaysia followed him, instead of their government, to change money into dollars,” said Sun. “China is different – all the major banks listen to the government, the majority of financial assets are in state hands, and a meeting with the financial bosses can put all of them on the same line.”