Copper is actually ~25-250X leas efficient at transferring heat than a heat pipe and convection is hundreds of times more efficient than radiation at transferring heat and the fins on a heat sink would have hundreds of times less surface area for dissipating heat all that is to say this might work but it would be orders of magnitude less efficient than a standard heat sink.
That’s the joke.
I assume the joke was either how expensive or how heavy it would be.