I think you touch on the most important question... The FAA requires a BACK UP electrical supply, for a very short period should all else fail.
The Batteries have no chance of pressurizing the Hull, and the requirement is for five minutes of service, roughly enough time to get the humans down to breathable air from flight levels, in an emergency.
It is looking more and more like the 787 engineering scheme is to incorporate a back up system into a sustainable part of the in flight regime of systemic electrical supply. If so, they violate the purpose of the regulations from my point of view.
Its not really different to any other a/c.
The Main Battery is there to ensure continuity to certain systems in the event of total electrical failure (Engines out for example) until the backup systems kick in IE. RAT/APU.
In addition because the brakes are electric, there needs to be a store of power to bring the a/c to a stop after a succesful emergency landing. The RAT will be of no use as airspeed drops on roll out so the battery power is used.
To put it into comparison with the 777.
The APU has electrical and pneumatic starters, so even if electrics is lost, bleed air will start the APU, The Battery is still there to keep standby instruments going of course until the RAT drops and powers up.
As for the brakes, hydraulic back up is from an accumulator (compressed gas).