Thinking about how an extrusion die is made, I imagine it's tricky to make very thin fins and to put them very close together. Copper work-hardens significantly too, which may be a factor.
Copper doesn’t extrude well for small parts for reasons note, as well as it’s overall strength is quite high - yield strength of 20k psi, tensile strength of 32k psi. and it has a pretty high melting and annealing point.
Extruding non-trivially sized parts starts to require some rather extreme equipment quickly, but is done for larger bulk electrical components, pipes, and tubes.
Aluminum heat sinks are extruded regularly. Aluminum tends to be used where heat sinking requirements are less severe, as it has less ideal thermal properties. A lot cheaper though.
If someone is paying the premium for copper, they probably want maximum thermal performance - which also means maximum surface area hence more and thinner fins (as long as the material is thermally conductive enough to keep them ‘fed’ with heat anyway).
