Why are cables rated for current not power?
Resistors are all the same size no matter the resistance. It's convenient for the manufacturer to test how much power a certain-sized resistor can take before it burns up. And it's the same for all resistors of that size. Also the power rating is the same regardless of the resistor's exact resistance (within the tolerance).
Cables with different current ratings are different sizes, so there's no such shortcut.
But actually, cables aren't usually rated for current. They're rated for their size, maximum temperature, and resistance, and you have to look up the current for that size, and you'll find a different answer depending on whether the wire is on its own, or in a bundle of other wires, or in a conduit, etc. That's because it's really the temperature that matters, not the current.