Was the intended story for the the Discworld's City Watch sub-series different than what we got? [Spoilers for City Watch Series)

I'm re-reading the City Watch series via the new audiobook (pro-tip, listen to them at 1.2x-1.3x - I really disliked them when I listened at 1x, but speeding it up a bit really improved them). And I can't help but feel like STP went into the series with an entirely different expectation of what he was going to be writing about.

I'm talking, of course, about Carrot. Now obviously, anyone whose familiar with Sir Terry Pratchett's writing style knows that Carrot was never going to be crowned King of Ankh Morpork. His story was, right from the get-go very clearly supposed to be a subversion of the old "Long lost king from humble origins saves the city and comes into his crown" trope.

I still do get the impression though, that Carrot was planned to be the main protagonist of the series, and that Pratchett just fell in love with Vimes as a character early on and pivoted. It sure seems like the original plan was for Carrot to eventually wind up as the commander of the City Watch, with Vimes retiring, which would play into the theme of Carrot's character that he can do the most good for the city by not being King.

But it reads as though along the way Pratchett saw the potential in Vimes and had so much fun writing his character that he changed his mind. It would explain why by the final few books in the City Watch series, Carrot goes from having one of the largest shares of "screen time" to being a barely present side-character.

Thoughts?

Side Note - anyone else catch the multi-layer pune (or play on words) for Carrot's name?

A Carrot is an orange (see hair color) vegetable that grows underground until it is plucked out from underneath the soil to fulfill it's true purpose

And

Carat as in diamond, as in diamond in the rough, as he's a King living amongst "commoners"