I realize I'm coming to this thread a bit late, though hopefully not all that late. A few comments:
Carrot's development: While he still believes the best about people he is different from the country boy from Guards! Guards!. For example he acknowledges that the Thieves Guild is an institution that promotes the well-being of the city and as things stand the Watch has to coexist with the licensed thieves and let them go about their business - despite the fact that he doesn't like it. Carrot is at his deepest in Feet of Clay, with his interactions with Dorfl and towards the end of The Fifth Elephant, when he makes his promise to Angua. The problem with Carrot's development is that there are places where it is hard to know how much he understands why his tactics work - for example when he plays the gambit in the Fool's Guild - did he realize the fools would think they were being threatened?
On the other board I once raised my little theory that Carrot, Vimes and Vetinari are in a way an urban male equivalent to the maiden, mother, crone trio. Carrot always retains a bit of the simple idealist, Vimes who takes care of the widows and orphans of watchmen and who is good at teaching watchmen how to walk was a father figure well before his son was born and Vetinari - well, you know.
Edward d'Eath vs Cruces:
Edward was an idealist. He was upset that Vetinari was changing the power structure in the city by letting members of working-class professions (such as plumbers) form guilds and thus gain a voice in the council of the guilds. He really believed going back to the good old days and having a king in charge would make things better. If Carrot had agreed to be king he would have followed him and obeyed him sincerely. Cruces was purely after power, and d'Eath's story was what gave him the opportunity to act. If Carrot had become king, Cruces would ave wanted him as his puppet.
The backstory about Vetinari supporting more guilds is part of the story about the economical and political change Vetianri had been pushing in Ankh Morpork all the time (though things only started seriously picking up with the invention of the clacks and printing). The old noble families are unhappy, but they are for the most part helpless to stop the changes.