He's not doing anything wrong.
There is little to no difference between copper and aluminium where the radiator
Copper has better heat conductivity, but as QuietOC said, the low heat conductivity of air is the biggest factor here, you will benefit much more from bigger surface area than radiator material.
In this thread
is a comparison between copper, aluminium and even perspex/pyrex glass (sorry for the error in my second post, corrected in the third). The setup in the thread is a radiating submerged PC in oil with different materials for the case, but a radiator in a watercooled setup will have to dissipate the same amount of heat so the same physics apply:
I was aware of the thermal conductivities of copper vs aluminum, but I had no idea that they would perform nearly identically in this scenario. I guess it is because the thermal resistance of copper and aluminum are both quite low compared to the thermal resistance of air which is the final destination of the heat energy.
I guess the analogy is that of choosing between two resistors, a 1ohm and a 2ohm, to hook up in series with a 2000 ohm resistor. It doesn't matter whether you choose the 1 ohm or 2 ohm, the 2000 ohm is going to dominate.
We know that using copper radiator can avoid the galvanic corrosion with the aluminum component.
This only goes if the other components are copper as well. Both copper and aluminium in the same loop needs an additive in the water in order to prevent corrosion.