I do not understand why people think killing penalties is the apotheosis of defensive play. Pavel Bure was notoriously awful defensively and killed penalties. Meanwhile Holik was great defensively and hardly did it in New Jersey. It's just a totally different game 4v5, but any forward can do it, especially used as Kovalchuk was, late in penalty kills, and almost always changing on the fly.
That said, Kovalchuk didn't transform - they got him to skate around in the D zone without the puck. That was an alteration to his game for sure, as he used to stand almost stationary waiting for the correct breakout pass, but Kovalchuk was still lousy defensively and a terrible F1 forechecker, which also impacted his defense.