I always have a laugh at this topic. The fact that there is thousands of miles of wire and components and microwave links and active components and tubes and transistors and SMD devices and recording machines between the guitar microphone and the loud speaker that YOU are listening to, yet those few inches of wire inside the guitar are somehow magical and are the only ones that affect the tone of a guitar... Oh 'Sweet home Alabama'... please save me...

Don't get me wrong. There is a sweet symphony between a player, their guitar, their pedals and amp that goes into creating any tone.. but much of the intervening stuff is insignificant. Gauge of hookup wire and brand of pots are very low on the list.

Within a pickup the gauge is hugely important. The thicker the gauge the fewer the winds and a resultant change in inter-winding capacitance and induced voltage at the output. More winding's gives more output, more inductance and more inter-winding capacitance, and thus a different sound. Same goes for different types of magnets... But once that signal leaves that pickup it is what it is until it hits a pedal or input of an amp (curly guitar cords and super long guitar cords excepted)

The main factors in the choice of hookup wire within any guitar are as Simon indicated. Physical strength and mechanical durability. Thin wire will flex, thicker gauge wire will not. The same argument can be used for pots... The shafts of cheaper ones made with pot-metal will often wear and fail earlier, more expensive brass made pots will often last decades. The quality and durability of the resistive and wiper elements of the pots will often be reflected in the price with the better versions being more expensive. It is an important consideration in choice of volume pot due their heavy use, though not so much for tone pots which are often set and forget.

So, the choice of hookup wire is entirely up to the guitar builder. Everything that is likely to be used will be of heavier gauge than what is used inside the pickups used, so it becomes more a issue of convenience to the guitar builder and how much Mojo the builder wants to spend/include in their build. (I cast a sideways look at my Gibson LP with a PCB connecting all the pots, due "consistency of manufacturing quality").... Same goes for the pots, where more expensive pots will often give more consistent performance results though with nil difference in tone... How you wire them pots up, the choice of pickups themselves and a possible inclusion of a 'treble bleed' circuit will have far more effect on that guitars tone.