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It doesn't make sense to me turning off the power failure feature would have anything to do with the machine powering itself up after specifically being told to shut down.
To me, it made sense because having flaky power can make the computer "think" it had lost power which could result in it starting up when the power is good. But it's been a long time since I used a desktop Mac as my main machine so I could be very wrong. But I thought it would be interesting nonetheless to explore non obvious causes :)
 
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