I take issue with rule, # 1 as well. Not all humanoids are cool mascots, but if the humanoid is of historic origin or regionally significant, it is usually pretty cool in my book.
Seminoles
Utes
Steelers
Boilermakers
Miners
Vandals (not that there is any tie to Idaho, but any team naming itself after an ancient barbarian horde that sacked Rome has my vote of approval)
Rebels
Cavaliers (UVA's sabers make for one cool logo too)
Volunteers
Jayhawks
Cornhuskers
Fighting Irish
On the other hand, some humanoid mascots are just too generic to be cool, such as
Cowboys
Redskins
Mountaineers (they get some credit because their mascot is just a filthy coon-*** that looks like he slept in a tree, who some out and fires a musket into the air - haw badass is that?)
Aggy
I agree on the inanimate objects thing, weather phenomana/music genres. That is so bush league/wnba/soccer.