If you have a nuclear reaction that is going out of control, then you have to get it in control. Shutting the plant down would mean you don't have the ability to use things like the control rods to do this.
No, the control rods are constantly forced into the core by passive systems (hydraulic pressure, gravity, springs), and only stay withdrawn because of active systems. If the active systems lose power, a few seconds later the control rods will be fully inserted. Many reactors also have pre-pressurized tanks of neutron absorbing fluid connected to the core, a sort of liquid control rod. Provided one of the redundant valves can be opened, that will also quench the nuclear chain reaction. (And I wouldn't be surprised to learn that the valves have a ratchet that makes them stick open until some poor bastard visits them in person with a special tool.)
It's also worth pointing out that many safety systems have no self-protection features like circuit breakers, or even off switches where a well-meaning idiot might turn them off just because fire is shooting out. If a back-up cooling pump develops a short circuit or a bad bearing, it will continue to run until it destroys itself. The idea is that the protection equipment will cheerfully use itself up to protect the main plant.