Here is a model I saw recently. Except I am the one who has used the AS-AD framework to illustrate that model.
The AD curve is drawn under the assumption that the central bank holds the nominal interest rate fixed.
According to that model:
If wages are sticky (so we are on the SRAS) a decrease in AD (the leftward shift from the red to the pink AD curve) will cause a fall in output and employment. OK.
But if wages are perfectly flexible (so we are on the LRAS) the same decrease in AD will cause an increase in inflation.
The author notes that this result is "counterintuitive", and says that more research is needed into the question of wage-determination.
Anyone familiar with the AS-AD framework would immediately see the problem and start asking questions about the stability of the equilibrium under flexible wages, and would recognise that you usually get counterintuitive comparative statics results if the equilibrium is unstable.
Here we go again. God this is depressing.
This is why we must continue to teach AS-AD and make sure that nobody gets out of an economics PhD program without seeing it and understanding it.
Otherwise they might end up running US monetary policy, and pulling the levers the wrong way.