The final linkages in the “mechanism” are those that connect changes in financial behaviour to changes in spending on real goods and services. And while high enough interest rates really can, more or less, force people to curtail their borrowing and spending, low rates can’t make them borrow and spend. They have to want to.
The power of monetary policy to boost domestic demand depends importantly on some sectors of the economy being in a position to respond to lower costs of debt, higher collateral values, reduced incentives to save and so on, by spending more today, with confidence that their income in the future will allow them to service and repay the debt.