Carrot and Angua have never seemed like the sort to have children, they both have a little too much inheritance to be comfortable passing it down, but if they did I suspect it would only be after very carefully, obviously, and publicly not getting married. There might be a signed affidavit of not-marriage involved. Because Carrot’s kids would be heirs to the throne of Ankh-Morpork and the city doesn’t really need heirs and although it might not fix everything a dose of inarguable illegitimacy would be a nice little roadblock in the smooth ascent of any possible monarch. It would certainly pose some trouble for any attempted kingmaker, especially if all the fiddly legal research was done beforehand. Plus, Angua still has a castle back home she’s probably technically the heir to and definitely doesn’t want. They’d be the only kids in the city with notarized documents kept in three locations explaining why they cannot legally inherit titles from Uberwald or Ankh-Morpork, with citations of long forgotten by-laws and apocrypha. Ventinari is just happy someone else is doing the work for him for once.