The simplicity of shutting down the pumps would have no safety-issue in a properly design system.
Many process control systems designers do levels of protection:
Level 3: Process Control
This level handles the normal operation of the plan. Regulates coolant flow to the pools and announces alarms if you get into a "high temp" state.
Most of the time Offshore in the oil business this level does not take any actions other than notifying the operator.
Level 2: Process Shutdown (PSD)
This level WILL take action on a "high high" event by starting redundant coolant pumps or other actions to cool down the material. This is automatic but usually take into account the speed of which the system could be normalized after a shutdown. This is primarily to protect equipment and not really the process.
Level 1: Emergency Shutdown (ESD)
Offshore this usually means a blow-down of pressurized systems and closing off wellheads. This is a hugely expensive thing... To be avoided!
This level ignores completely the cost of operation a trip will cause and is entirely about securing the systems and avoiding damage to people, environment and plant.
Thing is... Most people would refer to both PSD and ESD levels as 'backup systems' when in fact they are integral parts of the system design. PSD is something that happens routinely in most plants due to anything from equipment failure to network outages. It is what is supposed to happen when the normal operation is not stable. NOT NEWS....
ESD on the other hand usually makes the news over here due to the ramifications of a rig shutting down in an emergency.
So the fact that you can push a button and shut down a pump isnt really the issue. It should cause audible alarms of course, but you WANT to be able to kill off a pump rapidly if something unexpected happens.