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Oh and by making my head spin I mean, "once I throw doc, BG, and BP" in there too.

Mayor is a somewhat null balance role. It depends on proper knowledge of who is town to be effective.
BG is somewhat neutral as well, since the BG still dies. It again relies on knowing who is important.
BP is a town imbalance. If the player is never lynched, then it's basically a guaranteed doctor one time, but can be countered with strongman
Doctor is town imbalance, but can be countered with a roleblocker.

If both BG and Doc are town, it would require mafia to have a strongman kill not linked to a specific player and possibly a roleblocker on top of it.
If BP is town, it would require mafia to have even more power.

Unless of course, WoW did a bad job balancing the game, which is something I can't answer. (though I'm inclined to believe he did a great job)