I once wondered if it would be possible to have a nuclear power station which operated subcritically with extra neutrons injected from an outside source. The advantage I saw was that turning off the outside source would instantly stop the reaction, no worrying about articulating fuel rods and poison injectors. Unfortunately decay heat is still an issue.
Turns out it's potentially a thing but has some technical challenges.
As far as I know its not cost effective until the chain reaction starts so I don't think its possible to operate subcritically.
Thorium reactors can essentially do this safe shutdown as the fuel is a liquid rather than a solid so you can just dump the fuel and stop the reaction.
The problem is less about preventing criticality and more about handling the decay heat from all the isotopes produced when it was critical. That's going to give you 10% of the heat you had been producing with the reactor on for a little while after you stop the chain reaction.
Yes, that has been the common factor in most incidents. Chernobyl being the exception, they didn't manage even manage to get the control rods fully inserted before the shit hit the fan (poor reactor and control rod design).
Still, the British AGCRs were recently fitted with articulating control rods because if the reactor core was damaged they might not be able to insert them normally.
The Wikipedia page is a lot more detailed than I could hope to be, presumably you just turn off the power to the particle accelerator.
Existing safety measures rely on some degree of integrity in the reactor at the time they are triggered. If it gets too damaged before the control rods are inserted it may not be possible to insert them.
Turns out it's potentially a thing but has some technical challenges.