When it comes to powerlifting, it's probably better to start with less sport specificity and more overall volume. Simply put, you want to take advantage of the rapid progress you make in muscular gains at the beginning of your training career. This will, in turn, give you a higher ceiling further on down the road. Then, you might focus more on powerlifting specific movements and more volume in those movements. There will be plenty of time to hammer the squat/bench/deadlift, but you see way too many new "powerlifters" doing it from day one. I've known new lifters who were skinny and weak as fuck who did nothing but hammer the main lifts each day they were in the gym. You end up with lifters who still have no appreciable muscle mass or strength after a couple years of lifting.
Guys like Malanichev and other lifters of that level? Well, yeah, of course they focus mainly on sport specificity.
As for your last sentence, it depends. Sport specificity and where you put that increased training volume matters.