Whilst an a/c can dispatch with an inop APU, its Etops will certainly be compromised.
Because with a 50% reduction of electrical power following an engine failure on an all electrical a/c then load shedding would have to take place without the APU.
Don't forget the back up electrical hydaulic electrical pumps will kick in to pwr the lost engine driven hydraulic system just to add to the load problems.
So at this point it would be imperitive to land at the nearest suitable a/p. Hence the reduction in Etops capability with a U/S Apu.
People have a mistaken belief in the RAT, it is an emergancy pwr source of very modest pwr output, it certain will not give any output on ldg where electrical pwr is needed to stop the a/c.
An a/c can not dispatch without a servicable main battery, there are lots of vital services eg discharge of fire bottles etc where battery pwr is needed.
I said in an earlier posting that the removal of circa 150 batteries to date is very very significant. Only 2 caught fire so the rest must have been to under performing (low charge)??