It's interesting. I sense you responses are driven by the dull unimaginative repetitive sim engine failures. That's not the real world.
You're correct about ancillary systems. I know of one captain who 'nursed' a B767 home over a CAVOK Europe with 1 engine and reduced power. It was an ETOPS a/c within 2 hours of base and his defence was he hadn't shut down the other one; etc' etc. He was a very company man, got away wth it and no more was heard. I'm not wanting to open a whole new discussion about the right/wrong; just that the sim sessions are not so realistic.
Sim failures can not possibly cover all probable engine failures, both from time in session as well as practical limits of the simulation modes. But that is a broad subject.
On the other hand there is now a large amount of engine failure data that confirms the ability for the engine to continue to run stably with enough power for pumps and generators and in many cases to be able to be returned to some limited power.
As always follow your training unless that won't work and you're out of viable options