They US authorities on '60s started trying gravity on various types of reactors for many years (passive cooling) and it failed miserably all times. Download the excellent BBC's 1992 documentary on the subject A is for Atom, or watch it on YouTube.
It was after they had confirmed the problem that they started installing diesel generators to operate the cooling pumps. The problem was discovered also in USSR. Chernobyl erupted during an experiment to test the cooling apparatus while disconnecting the plant from grid.
The root cause of all this was that they designed the commercial Nuclear Plants by scaling the 60cm diameter Submarine Reactors into 3 meter or even more. That way, the multiplied the fuel mass x1000, and disregarded that fact they were no longer 100 meters deep below the ocean surface, something that would guarantee passive cooling simply by hydrostatic pressure.