Crys made some good points about how Vimes hates all the hoopla and politics that Vetinari has to endure. Vimes hasn't the patience for all that and only does it because he is FORCED to by Vetinari or Sybil. And he will get out of it if he has ANY chance to do so.
That wouldn't bide well for someone who may or may not succeed Vetinari.
Carrot is the only plausible successor of Vetinari.
But the truth is that Vetinari see everyone as tool for His use, He is very good at finding cracks in personalities and the right levers
Doesn't that sound like Carrot?... though Carrot does it ever so nicely and with less threat. Carrot also sees the study of people in a scientific way (but with heart too) and he is really fascinated with people and thier behaviour and why they do what they do.... and through this he gets people's confidence as part of his job in the Watch. All skills applicable as the Patrichian. He would be a likable and liked leader, and still get his own way just as Vetinari does.
And if he found out about his "connection" I feel he would "Do the right thing" because when it all comes down to it he is as devoted to the City as Vimes and Vetinari... perhaps even on a larger scale because he has the history of the dwarves/Koom Valley to encompass and I can see him reaching out beyond the City on a political level and take Ank-Morpork a step further. A human who followed the rules and fitted in to become a dwarf and who thinks of himself AS a dwarf first and foremost? He would fit in as the Patrichian just as easily. And as he has started out as a "man amongst the people" and with his tact and talent at getting people to do what he wants (politically) he can reach out on both levels.
As far as Vimes and Vetinari go... they compliment each other. They are neve enemies.
Years ago we had an analysis of our positions done in our office. My two supers and me. Its called the something or other triangle. One gets the nitty gritty done... all the major decisions fought for with the hierachy CEO's and everything laid out financially for the complete overview of the "City" and alot of politics involved with unions and the CEO's ; one was the DOER. Knew what had to be done and did it... hands on... (his 'watch' being a few hunded employees) and one was the facilitator... that was me. I made sure that what B. needed to make sure what A. wanted done was available and vice versa. (does that make me Drumknott?) no idea.
Interesting thread though.
The Collective Brain: The synoptic serendipity that comes when interesting thoughts from interesting and interested people get together. And the whole is always more than the sum of its parts.