Admittedly, not all boom/bust cycles are detrimental and have significant real effects. This is also one of the reasons why the mechanical targeting of asset prices is not a sensible option for monetary policy.
However, if we had a fully nationalised central bank, I would not be giving speeches suggesting that we privatise it. So why not just nationalise the SARB? Simple. It would not change anything useful that we cannot change anyway, and it would be expensive.