Espresso machines use pressurestat for steam boiler and a thermostat for the brew boiler.
But the temperature fluctuation is effecting the end result.
If you want a more stable and consisted result, you need a PID.
More control and stability plus less power consumption.
PID on espresso machines is like the cruise controll in cars, or autopilot in boats.
Some still use/prefer the old fashioned windvane(in boats) thermostats/pressurestats in espresso machines, normal playing with your foot on brakes instead of ABS, centrifugal governor instead of speed sensor/hall/tachometer . Its the same as using an old school thermometer with liquid rather than NTC.
So while thermostats have the simplicity and proved them selves for many decades now,which we can not deny or be thankful for that, but when you want to raise the effectiveness of your curent project weather it is car/boat/espresso machine etc, then you need to start fiddling with PIDs/cruisecontrolls/autopilots etc....