What does the thickness of the wire have to do with anything?

The thicker the wire, the lower the resistance.  The lower the resistance, the less power is lost in the wire in the form of heat.  Two reasons not to lose power:  You might want it for something else, like running all those accessories.  Also, the heat generated can shorten the life of the wire and the things connected to it, or start a fire, in extreme cases.  When sizing our wires, we use the National Electrical Code as a starting point.  Even though it is mostly for buildings and appliances, their current ratings for different wire gauges are a good rule of thumb.  For instance, The NEC says that 14ga wire is good for up to 15A.  All that means is that they consider that gauge of wire not to be a fire hazard, and have an acceptably small voltage drop, not to waste too much power.  But a heavier (smaller number) gauge always runs cooler and wastes less energy.

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