Several years ago when I got Thrawn signed by Zahn at Farpoint, when I handed him the book he asked me what I thought. I think Zahn expected an, "Oh, I liked it, it was good." Instead, I said, "I didn't expect a Sherlock Holmes novel, and I felt really dumb because I missed the obvious clue." Zahn stood up, handed me the book, looked me in the eye, and we had a conversation for two minutes about Thrawn as a Holmes (or Moriarty) figure, the obvious clue I missed (Nightswan/Cygnus), and translating the language of the GFFA into English. He held up the line for this conversation.
Thrawn works as a protagonist, imho, because he sees himself and acts as the hero in his story. He's not evil, I'm not even sure he counts as anti-heroic. In his mind, he wants to make the galaxy a better place for his people, and he judges the Empire to be the best route to achieve that. I think that always made him a compelling antagonist for the New Republic. I hesitate to use the word "villain" for Thrawn; he would disagree with the appellation entirely.
The difference between Thrawn and Holmes, though, is that Holmes's author allowed him to be fallible. For all that he seemed to be five steps ahead of everyone else, there were plenty of times when he realized what a fool he'd been for missing something critical. The issue for me was not that Thrawn saw himself as the hero -- it's that Zahn failed to give him any challenges that would test his heroism, because Thrawn already had every problem solved before you even started the chapter and it was just a case of watching his strategem unfold exactly as he'd foreseen it.
Heroes are defined by the quality of their enemies. The more the hero is outclassed by the villain, the more impressive their victory is -- which is why George Lucas pitted a farmboy and a space trucker against the concentrated military force of a galactic tyranny. But nobody outclassed Thrawn in the new-canon novels. He never faced a real challenge, he was never at any risk of failing, and he had nothing he needed to learn along the way. So the story just wasn't interesting. It was just watching him coast through life.