The FADEC knows a lot but not everything.
agree
it may tell on you but it's not there to punish you if you need it
lots of data over 50 years that engines can still run enough to generate hydraulics and electricity even with damage.
If you want to save the engine, that's your decision, but your aircraft is a lot more important.
The decision making is a lot easier in this regard when you've got at least one good engine still running. Things get a lot dicier when you got all sick engines and then you need to be careful dealing with one at a time.