One common free-market argument against government control over interest rates goes something like this:
The Federal Reserve should pull out of the interest rate manipulation business completely. Having a Fed whose main job, at least in the eyes of the public, is to set or move interest rates in centrally determined directions makes no more sense than having a powerful government agency determining what should be happening with any other price in the economy. If the Fed could know the right price for loanable funds, then there is no reason to think that they couldn’t also know the correct price for shoes, computers, or food. It is the fact that neither the Fed nor any other central authority can know the right price for any of these products, interest rates included, which makes efficient socialist central planning impossible.
In other words, they are arguing for some variant of free banking.
I find this to be a thorny issue to think clearly about. Theoretically, the free-market argument makes sense. But, on the other hand, we have nominal rigidity and the risks involved with change. Also, some governments are more competent than others — the right answer for Switzerland may be different than the right answer for Zimbabwe.
Note that I think the political feasibility is very low. Government control over the money supply seems to be a stable equilibrium. So this question is mostly of academic interest. But it might be relevant for, e.g., charter cities.
The Fed uses the short-term interest rate to either promote growth or fight inflation. The government has other methods to do this using fiscal policy and some MMT economists argue that the Fed should freeze interest rates at 0 and use fiscal policy instead for promoting growth by more fiscal spending or fighting inflation by raising taxes. If the free market was to determine interest rates without central bank intervention it would probably prefer growth and not fear inflation as growth benefits the market and companies and wealthy investors would offset inflation by rising prices and holding real assets. High inflation would lead to instability so it probably does make sense to have a government role in managing the economy to prevent instability.