Well, technically, he IS...........the best one in college sports, IMHO.
MASCOT, definition:
A person, animal, or object believed to bring good luck, especially one kept as the symbol of an organization such as a sports team.
The Chief appears to fit that definition you gave. The problem is the perception of folks who don't know any better. He is not a mascot in the sense that Bucky Badger or Herky Hawkeye is a mascot. He does not lead cheers, play with the kids, or get involved in wacky goal-posting. The Chief isn't on the field or court with the team at any time. He does not get involved with the crowd. The Chief is a four-minute demonstration at halftime. He is not whimsical or humorous. Chief Illiniwek is noble, proud, and respectful.
Those calling for the Chief's retirement do not have a clue about what he represents or the respectful manner in which he performs.
I prefer to refer to the Chief as a symbol, not a mascot. Calling him a mascot cheapens what he represents.
He may be a mascot by cold definition, but he is not like any other in all of college sports, and in my opinion should not be lumped in with the rest of them.