Interesting explanation thanks ! However, I think you made a mistake (probably a typo but I think it's worth noting it to avoid confusion of other readers) in

Interesting explanation thanks ! However, I think you made a mistake (probably a typo but I think it's worth noting it to avoid confusion of other readers) in that sentence: “However, if there isn't enough control material in the core that the proportion of FAST neutrons is enough to make the reactor critical”. Prompt neutron (short time between fission and neutron emission) should not be mistaken with fast neutron (high kinetic energy, see https://en.wikipedia.org/wiki/Neutron_temperature https://en.wikipedia.org/wiki/Neutron_temperature)