Here is your conceptual mistake. Using an arithmetic mean makes no sense here because you want to look at the individual miner and you do not want to include miners that are not mining)
Bob and Alice are still mining by spending 2 resources so they spend exactly the same as before but receive more.
Satoshi is no longer mining so he is spending 0 resources and receives no more coins (not that he needs them ;-) )

You are basically taking satoshi and adding him to your mining calculation which logically makes no sense.

[edit] do you see the problem in your assumption? I can add an infinite set of miners that do not mine (does not affect mining at all) and it would make your average miner spend close to 0...