My point is about how "binary" signals are controlled via modulation to emulate an analog variable for use with a continuous controller, not a recommendation to run your gas furnace this way. (That might have been lost because of the line the conversation followed).
In a real system this is exactly how MOSFETS are used to control a voltage; you would almost never use an analog amplifier for high power because of the losses, so voltage control is binary on/off, but that doesn't restrict you to just bang-bang control despite the GP's statement.
In fact, an electric heater can and often will be controlled via a PWM method with a continuous controller rather than via hysteresis.
In a real system this is exactly how MOSFETS are used to control a voltage; you would almost never use an analog amplifier for high power because of the losses, so voltage control is binary on/off, but that doesn't restrict you to just bang-bang control despite the GP's statement.
In fact, an electric heater can and often will be controlled via a PWM method with a continuous controller rather than via hysteresis.