Proportional Controllers not only save energy, they can give a controlled finish or treatment to a job. An on-off controller or thermostat limit protection has to be used in series, this is to to stop a Runaway Process.
There was a real life instance when a Temperature cycling oven maker (environment chamber), faced large liabilities as an 8086 based profile controller and chart recorder just locked up and all the electronic equipment were roasted. Here even a bimetallic thermostat would have saved the day. Nowadays we have a watchdog timer to prevent such uP mishaps, but still use an analog controller in series as an over temperature trip.
Other Reading
The basics of control system design: Part 1 – Moving beyond PID
“This series of six articles will explore the use of six variations of P, I, and D gains: Proportional Control, Proportional-Integral Control, Psueodo-derivative feedback with feed-forwared (PDFF), PID control, PID+ control, and Proportional Derivative Control.”