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Those electrical code cross sections are for 350A at 230V, corresponding to about 80 kW (400V is the same as it's actually three 230V wires).

Processors operate at about 1V. At 300W it's enough to use a much smaller cross section, which is split across many traces.

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That's not how I^2R losses work. Voltage is not relevant.

I agree. However voltage is relevant for insulation, which also affects how heat can dissipate for the wire, and might also be relevant for a failing wire, when higher and higher voltage can build up at the point of failure (not sure if it's a common engineering consideration outside of fuses, which are designed to fail).

At 300W there's only so much power that can become heat. With 80 kW flowing through the wire, if the insulation melts due to excessive wire resistance you call the fire brigade.

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