Autonomy is all well and good, but if you permit a FADEC to switch off an engine automagically, I'd like to see your PROOF that it can't turn off another.
I can't speak for the other guys, but on Boeing, there are only two cases where we let a FADEC unilaterally turn off an engine (other than during autostart). The first is electronic overspeed protection - if a rotor speed is significantly over redline and the engine is not responding, we shut it down to protect the structural integrity (burst rotor discs are potentially catastrophic - see Qantas A380). The second is when uncontrollable high thrust is detected on the ground. Thrust Control Malfunction Accommodation (TCMA) has very specific logic that if an engine is at high power with the throttle at/near idle, and the engine is not responding, it'll shut it down. It's inhibited in-flight (for what should be obvious reasons) with rather robust air/ground logic that defaults to air if the required inputs are invalid/unavailable.
TCMA was first implemented on the 777/GE90-115B and is basic on the 787, 747-8, and will be on the 737MAX and the 777X. Both the electronic overspeed and TCMA are to meet mandatory regulatory requirements (FAA and EASA).
We intentionally do not cross talk data between the different engine FADECs to maintain engine to engine isolation.
BTW, while I assume automagically is a typo, it did make me smile...