In the 2 airlines I have worked for that operated B737NG’s, no N1 OR N2 rotation was considered a severe damage condition.
Remember the ENG FAIL annunciation is triggered solely by N2 falling below sustainable idle (approx 50%) with the associated start lever in idle. That’s it, there is no clever science behind the annunciation. In isolation, it indicates a flameout or some other ‘innocuous’ failure, where a subsequent restart can be attempted.
ENG FAIL associated with other indications suggesting seizure, separation, abnormal vibration etc require immediate action, I.e. run the severe damage or separation memory items.