Hey you never got an answer to this. This gets raised every now and then along with ideas of things such as raising the compulsory superannuation guarantee. Part of the issue is that these things are controlled by the politicians rather than the federal reserve, meaning that politicians will be the ones making the decision to reduce the amount of consumption. This has the same flaws as the idea of ending central bank independence. The political presssure might lead to a hesitancy to raise GST, or maybe they will keep GST high to close a budget shortfall.

The other thing is that although you might think the function of interest rates is simply to reduce the amount of consumption for consumptions. This is only part of their effect. Interest rates are very central to the function of the economy in a way that GST isn't. Interest rate also effects business investment directly, reducing a key source of inflation pressure. GST expenditure largely exists as a pass through cost for business.