From the technical news they said they had to increase the number of cores to reach their efficiency target.
They lowered the frequency from 1.5Ghz to 1Ghz.
I thought this would mean if I don´t care about the efficiency I should run it at 1.5Ghz with a stronger PSU. However Black Arrow software says this would not be possible.
Why not? Does it have to do with cooling?
I drew the same conclusion as you but with a few caveats: not only would you need to be able to supply the power (meaning not only the PSU, but also the PCBs and VRMs need to be handle it), you must also be able to get rid of the heat. Moreover, BA would have to provide ways to change voltage and clockspeed. If they say its not possible (didnt read that, but Ill take your word for it), Im guessing thats where the problem will lie.
Of course anyone designing their own PCB and just buying chips from BA might be able to leverage some of that headroom, though its probably not going to be a walk in the park.