They have to shut down during the earthquake to ensure they maintain coolable geometries. Cooling is easier at lower power.

Some Fukushima reactors did have some self-powered safety features, like a little steam turbine that comes from the boiling coolant and is hooked to a coolant pump. These features are at least a little related to why some reactors failed at different times than others in Fukushima.

But seriously, there is enough decay heat to do more of this so it's a pretty good point.