You seem to have decided to cut the part that follows.
"Having ESRAM costs very little power and has the opportunity to give you very high bandwidth. You can reduce the bandwidth on external memory - that saves a lot of power consumption"
Why did you cut that?
Anyway look, Obviously the PS4 shutdown and couldnt be used for awhile due to heat.
I intentionally cut out the second part because it makes the whole statement even more ridiculous. Fact is, MS went with high speed ddr3 ram (2166MHz, not the cheaper and less power hungry 1600MHz ram). Obviously they thought they would need the hotter ram/higher bandwidth. And adding the esram obviously increases power consumption further...
Just read the data sheets. The memory in the PS4 uses LESS power than the memory in the XBox One. Had Sony gone with 4G of ram only, maybe the equation would be the other way round (didn't check, too lazy and it doesn't matter anyways).
And what do you mean by "couldnt be used for awhile due to heat"?
Two seconds is now awhile? I don't know how long it takes to retrain the gddr5 chips and get everything else running again, but two seconds of waiting seems like an excellent trade off if it saves the PS4 from a self destruct. I'd call that excellent engineering foresight.
What I would be more interested in is knowing whether the PS4 saved the state of the machine (eg you can continue playing the game where you sort of "left") before shutting down or whether it was an emergency shutdown (like on overheating pc graphics cards).