I don't think what you said supports what you mean. Yes fossil fuel consumption goes down in crises. The problem is they are crises. Temporary until new energy comes online.
I think I follow the population growthrate changes, but even aging out our populations with status quo is why I said by the time we get there to permanently shrink fossil fuel use, we'll be at +4°C and well have other factors affecting population and consumption. None of which are desirable.