I would argue that the "brunt" is borne by the thing with intelligence i.e the control plane. The control plane which is some general purpose CPU running Linux

I would argue that the "brunt" is borne by the thing with intelligence i.e the control plane. The control plane which is some general purpose CPU running Linux/VxWorks(Cisco)/FreeBSD(Juniper)is what builds the FIB and actually populates those ASICs in the forwarding plane. The ASICs are basically just lookup tables that rely on data pushed to them by the control plane. In other words they rely on computation/preprocessing done elsewhere.