Why are AWG charts rated in amperes and not in watts?
Current flowing in the wire heats it via resistive losses (RI^2).
What determines the usual wire gauge current ratings is basically how much resistive heating it can take before the heat damages the insulation. Thus a wire inside a conduit without any airflow can safely conduct much less current than a wire cooled by the airflow of a fan. Likewise an uninsulated wire, or a enameled wire, can withstand a higher temperature therefore higher current, because the insulation (or lack thereof) withstands higher temperatures.
Wattage doesn't matter, since power is volts*amps, and volts don't heat wires, amps do.