Terry loved his characters in a way that's hard to express - unless they were pure evil (and he had a few) he did his best to understand their motivations in such a way that he came to portray them sympathetically.
This is most noticeable in his caricatures that became characters that became badasses over multiple novels; the Watch has a few of these, but there are others.
Yup. Vimes going full-on berserker mode while screaming "Where is my cow?" should, by all rights, be extremely silly. Instead, it sent shivers down my spine.