For other's curious: the "load resistance matches source resistance" is true for maximum power transfer of fixed voltage sources. In the case of current capacity of a wire, the voltage is variable, but the maximum current is fixed.
In that case we are selecting the input voltage for maximum power so (Rs, I are fixed, Rl can vary, and for a purely resistive load, Vin is a function of Rl):
Vin=I(Rs+Rl)
Vin = Vs + Vl
Vl/Vs=Rl/Rs
Pl = (I^2*Rl)
Clearly we can always select a Rl (and thus a Vin) that gets the desired Pl at a fixed current. Obviously at some point we are limited by shielding of the wire, and DC/DC conversion at the end-point. We eventually may also be limited by interactions between the medium surrounding the wire and EM fields generated by turning the circuit on and off. But, when you can control the voltage, there's no simple calculation from wire impedance to X maximum watts of load.
In that case we are selecting the input voltage for maximum power so (Rs, I are fixed, Rl can vary, and for a purely resistive load, Vin is a function of Rl):
Clearly we can always select a Rl (and thus a Vin) that gets the desired Pl at a fixed current. Obviously at some point we are limited by shielding of the wire, and DC/DC conversion at the end-point. We eventually may also be limited by interactions between the medium surrounding the wire and EM fields generated by turning the circuit on and off. But, when you can control the voltage, there's no simple calculation from wire impedance to X maximum watts of load.