Actually a very good question.
In principle, yes the hardware could be completely self sufficient for power management.
In practice, however, making the right power management decisions usually requires knowledge outside what the GPU or CPU has available. As an off-the-top-of-my-head example, you want to power down the 3D engine very aggressively when there is no drawing activity, but if your game stalls while swapping in a big texture you probably would *not* want to power down the 3D engine in that case. That decision heuristic would require that power management for the GPU be cognizant of disk activity.
The preferred approach for managing power is also changing over time, with a slight trend from "run the hardware as slowly as possible while maintaining acceptable performance" to "run at full speed, get the work done fast and then switch everything off as quickly as possible until more work comes along". As you can imagine, it helps a lot of the CPU and GPU power management follow the same approach
When setting memory clocks you need to make some pretty complex bandwidth and latency calculations in order to make sure that the display fifos don't get starved for data when the 3D engine is drawing into the same memory. One implication of this is that the minimum memory clock setting is a function of engine clock, drawing activity, number of active displays, depth / resolution / refresh rate.
Since changing clocks takes a non-trivial amount of time (you need to let the PLLs in the clock generators settle at the new frequency after changing dividers) you need to include recent behaviour trends in the decision-making logic, not just what is happening at this instant, in order to avoid too-frequent changes with the associated waste of power and time. All of this can be done in hardware but you can see how quickly the complexity can grow.
Anyways, bottom line is getting the very best power efficiency always seems to require making decisions using more information than what is available to each individual device, ie shifting from focusing on device power management to focusing on platform power management.