I'm pretty sure that's exactly how Pterry intended it. I don't remember where I read it so take it with a pinch of salt, but Pratchett himself has confirmed this, pivoting to Vimes as main character for the City Watch when Carrot was intended to be the one.

And I'm glad. Carrot is a great side character to compliment Vimes, but I feel he'd be fairly one-note as a main character. In Guards, Guards! we kind of need Carrot to introduce the situation to us, but Vimes has so much depth that I'm glad he became the MC.

I also like that it makes Carrot more mysterious. We're never quite sure what's going in his head, and that makes him much more interesting.

Edit: It's in The Art of Discworld:

Vimes was never intended to be a major character; I began the first draft of Guards! Guards! with the assumption that Captain Carrot would be the lead. He was, in a way, but only in the sense that Zeppo Marx plays the lead in a Marx Brothers movie; technically he sometimes did, but no one ever went to see a movie just because Zeppo was in it. I needed a head to get into, and Vimes’s was empty at the time, so suddenly we began to hear his thoughts…

I'm the exact opposite. I love Skyrim and Oblivion, but just couldn't get into any of the Fallout games I've tried. I liked the Fallout games in a mechanical standpoint but I've never liked the post-apocalyptic genre so I just can't keep interested.