Why do consumer ovens use thermostats instead of PID + PWM?
Mechanical thermostats are capable of switching high currents with very long life in that application. They are inexpensive and accurate enough. They don't mind the high ambient temperatures and don't require cooling fans or heat sinks.  The technology is mature, and can be produced by automated lines. They don't tend to fail 'on' and cause damage or fires. The short-term variations in the air temperature are not a hindrance to competent cooking.
Yes, you could replace the thermostat (or slow-switching relays controlled by electronics as in our oven) with more sophisticated controls and phase-controlled heaters or something like that and it would keep short term variations in air temperature down, but why would you if it doesn't matter?
And it would not aid recovery- might slow it if the controller is tuned to avoid overshoot at the expense of rise time. Best-case recovery is related to control authority, not the controller. When the temperature drops with an on/off controller, the heater(s) go on 100%, you can't get any better than that.
That's typically the limitation in real control systems- a PID controller could in theory turn a battleship on a dime, but the amount of power required of the engines just isn't there to make that happen.