This might be a hot take but, I'm convinced that Carrot wouldn't be the one to take over command of the watch after Vimes retires. It'd be Angua. She and Vimes are so similar, both in temperament and worldview, and just the way they handle police-related problems.
Like. That's such a Vimes way of looking at things. And much like him, she doesn't let her cynicism stop her from doing her job, she uses it as fuel. She doesn't have the same ties to Ankh-Morpork that Vimes does, but she's fiercely loyal to Carrot, who effectively *is* the city.
And the bit at the end of men at arms where Carrot himself explains to Vetinari why it shouldn't be him commanding the watch - people should follow orders because they're given by a commanding officer, not because they're given by Carrot. Angua doesn't have that charisma that makes people like her and do what she says; she just has intelligence and willpower and a good, disillusioned understanding of how people work. Not to mention all the thematic parallels we see between her and vimes and their struggles with restraining their inner beast (literal or metaphorical).
Idk, it seems such an obvious choice to me. I think if Vimes ever managed to actually retire, the only person in whose hands (paws?) he'd be comfortable leaving the watch would be her.
(also the post of commander comes with the title of Knight and "sir Angua" would be hot as fuck)