[rogersnm]

> how would higher prices change anything about that?

Higher prices reflect a new equilibrium between the quantity of money and the quantity of goods and services being produced. Until that revised equilibrium is reached, you generally suffer from shortages of goods and rising prices.

> It's still very much in the system, the money supply hasn't changed at all.

The money supply doesn't need to decrease for inflation to stop, it just needs to stop increasing on an output-adjusted basis (and even then you need to wait for the equilibrium to be roughly reached before price levels stabilise).