The conclusion will be the same whatever the task or the active core count, best efficency in respect of battery life is when CPU power is equal to rest of system power, that s mathematicaly provable..
It is not true in general. It is only true in some designs.
Consider a design that uses very little power outside of the CPU, e.g. 1W. What if the CPU needs to run at 1GHz to use 1W but it can run up to 2GHz on the same voltage? Such a CPU will use 2W at 2GHz. Now you can run your CPU at 1GHz and the design will use 2W. Or you can run it at 2GHz and it will use 3W. Which one is more efficient?
(The above ignores the leakage which does not scale with frequency. I.e. such a CPU at 2GHz will use even less than 2W, depending on how much can be attributed to the leakage.)
Obviously, the frequency/voltage curve often means that you cannot double your frequency at only twice the power consumption. However, you cannot just say "it is mathematically provable that a design that uses half its power on the CPU is the most efficient". Or you can say it when you provide such a proof
There are far too many variables (frequency/voltage curve, leakage, ...) for there to be one single solution to this. It depends on the design.