When most of the hydrogen in the core of a massive star has fused to form helium, the next fusion stages (helium, carbon, neon, oxygen, ...) produce less and less energy in a single fusion reaction. As a consequence, the later stages last shorter and shorter. This is often explained by saying that the power output must remain constant.
This explanation seems to assume that the star (or it's core) must remain in some form of equilibrium. Why equilibrium? Why can't the total power output decrease because of the lower energy from a single fusion reaction?
My guess: if the core's luminosity decreases, the core will contract and become hotter and denser, which accelerates the fusion reactions in the core. Is this correct?