AusFinance

There already is. The RBA only sets the "cash rate". Your mortgage isn't at the cash rate, and neither are the loans businesses take out. They're influenced by it, and a lot of banks will essentially have their rates rise and fall in lockstep with it, especially for regular people who don't have the negotiating power to lock in special agreements, but they don't have to.

That's kind of the case in the US. They don't have variable-rate home loans, so only business borrowing is affected by the US Federal Reserve's interest rate.