An Alpha's enraged kill is much like a militias single shot, often debated for best use (only got one) before they get killed off.No matter the case, it comes down to the Alpha's judgement on when to use.
Some other instances for Alpha Rage kill
1.Click happy...what this do (random player dies)
2.I don't like you for some reason....you now dead (selected personal "rival" dead)
3.hide a shift.....Two kills one real shift other to make it seem like decoy was real SS (make players look for decoy not your fellow wolf)
4.Looks like they are on to me.....I'm going to use it and take someone with me to the GY.
- extra death makes it seem Omega still alive/ was killing wolf even if not