1. I don't think we're actually talking about that much power, in most instances the issues amount to "not behaving professionally in an environment that wants to have a professional character"
2. What would it need to be for you to consider what power it gives as "earned"? I'm surprised since it seems that power being explicitly delegated by the project should be enough by any measure.
Actually this time it's the opposite. The moderators' refusal to elaborate unfortunately lends itself to your position and it was my knee-jerk reaction too until I found out the conjunctured details.