I think we are just missing the point.
‘Quality’ affect performance...like better octane petrol could improve the performance of a car, better electricity has the potential to increase the performance of an electrical equipment.
Hot water cylinders are very old technology, a new one and a 50 year old are pretty much the same, well not really...old ones used better materials (copper) Their thermostat and element isn’t a precise and perfectly tuned computer, they also slowly deteriorate due to their own working environment (water, heat, etc).
The thermostat sets a maximum limit for the hot water temperature, it does not fully control temperature, by law further regulation has to be done by using a tempering valve and manually testing the water using a thermometer.
As a plumber I don’t remember ever finding even a new cylinder were the temperature set in the internal thermostat and the temperature of the tap water to be a perfect match. (Usually less even by 10 degree Celsius) External variables, like water pipes, humidity, weather, season, etc. Will make this hardly possible.)
I believe better power electricity in fact could increase the temperature of your hot water in the same way it could affect the saturation and brightness of your screen or the loudness and background noise of your stereo. Thanks