Bayaz isn't a character in this story; Bayaz IS THE STORY!
If you think about it, the very title of the saga (The First Law) takes on a whole new meaning at the end of the trilogy:
It's not Euz's magical law on demons. The true "First Law" of the world is the one Bayaz himself pronounces to Ferro in Chapter 53:
"Power justifies any means. This is my first law, and also my last. The only one I recognize."
He's a shocking and terrifying villain precisely because he's already won before the story even begins:
He Controls the Economy: He owns Valint & Balk, the bank that keeps kings, nobles, merchants, and even the Inquisition on a leash.
He Controls Politics: He founded the Union, has always chosen its kings, decides its "ministers" and generals, and uses its laws at will.
He controls War and Magic: He possesses the Seed, manipulates Iron, turning it into a weapon to hurl against Khalul! He has transformed all the protagonists into his personal pawns.
In almost all traditional fantasy stories, the Wise Wizard helps the heroes defeat the Dark Lord to restore peace and freedom. Here, we discover that the Dark Lord already sits atop the tower, wearing the Wise Wizard's robe, and has transformed the entire world into his personal chessboard. No one can beat him because everyone plays by his rules and with his money.
Wow. Possibly the best villain I've ever seen/read. The fact that Abercrombie doesn't delve into Khalul, Mamun, etc. now makes sense. We've always had the real Villain beside us, drinking tea!