Running a core doesn't only run the core itself. There is a fair amount of supporting circuits including, but not limited to, things like memory controller, I/O

Running a core doesn't only run the core itself. There is a fair amount of supporting circuits including, but not limited to, things like memory controller, I/O bus, peripherals, etc. These can sip a non-trivial amount of power, and if a task running on an efficiency core kept them all up, you ultimately might end up with greater aggregate power use. Nowadays in modern chips these other circuits seem to be brought down to the low power states much more aggressively.