"Why do the central bank control monetary policy, but the government control fiscal policy?"

As of 1997, monetary policy has been independent from the government in order to remove any political bias or influence from the decision making. The government often had the habit of reducing interest rates prior to elections in order to boost spending and consumer confidence, thereby winning votes, and then raising interest rates once elected. This is unsustainable and can lead to excess inflation and instability, and hence the setting of interest rates was made independent.
Furthermore, this essentially reduces the scope and extent of government intervention in the economy, allowing the government to use its time and resources more effectively on fiscal policy.