Karkat lives full time at the WCT base because he has nowhere else to go. He's been there for a year, having been introduced to the base in early 2013 by CONDOR agents because they were politically obliged to see he was taken care of had nowhere else to put him and they figured teenagers would have better luck dealing with him than adults. However, he's still in-training because he didn't get cooperative enough to start using the training facilities or listening to the others until about six months ago (plus he doesn't have any powers and his existing fighting style, if one could call it a fighting style, was less 'incapacitate someone doing a crime without killing them' and more 'extricate yourself from a possibly lethal situation and murder your assailant if you can'). He has probably been on a few basic crime stoppin' excursions and patrols but nothing with an actual supervillain – the closest he's come to that kind of thing is that on about three separate occasions he has wound up getting kidnapped by generic bad guys who want to lure the rest of the Trailblazers into a trap because he's easy to spot and easy to capture.

Because Alternians aren't ultra popular with humans, and because of the kidnapping thing, Karkat spends a fair amount of time indoors at the base, training, watching sappy movies, and grossing up the place with his dubious culinary choices, like some kind of stocky, bad tempered Starfire. Everybody on the team is in some capacity his friend whether they like it or not.