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Consider a generic single phase AC 240 V (or 125V) device for home use such as a hair dryer.
From a purely functional point of view, what difference does it make if a phase is switched with the neutral on the supply terminals?
From a safety point of view I understand that there are safety implications.
Generally none. If it were not so then a single-pole switch could not be used on an appliance with a reversible mains plug. Since electrical current flows in a closed circuit an interruption or break anywhere in the loop will switch the load off.
simulate this circuit – Schematic created using CircuitLab
Figure 1. Live-side and neutral-side switching.
Having the switch on the live wire is safer. If you take your hair-drier, for example, consider what the situation would be if it fell apart in your hand exposing the heating element. A switch in the live wire would isolate the element from the live feed whereas a switch in the neutral would not.
For the hair dryer, it does not matter, and it must not matter. This is because there are countries with unpolarized plugs so no device can assume which device is live and which neutral, as you can plug it in both ways.
