I do like Kovalchuk as a player, he produces and shows up every single night, always had the potential to be the one who carried the team, but he's never been that guy in the NHL. Most of the time in his NHL career he missed the playoffs a lot.
He had two early exits with both New Jersey and Atlanta, Atlanta in 2007 didn't really have high expectations but that team was pretty damn good, but thought that year they had strong potential to advance to the second round. The Devils in 2010 were expected to maybe be one of the cup favourites, along with Chicago and Washington, but were out in five games to seventh seed Philadelphia. First team out as well.
In 2012 sure the Devils made the finals, in fact Kovalchuk did lead the team in points in both the regular and post-season. But the Devils had an easy ride to the finals if you ask me. Florida was overrated that year, Philadelphia I found to be shaky, NYR was their big challenge, and they lost to the Kings which were the eighth-seeded team. Although, nobody expected the Kings and Devils to be in the finals that year.
But in 2013 after Parise left, Kovy could barely carry the Devils.
On his teams in Russia he did do amazing, but SKA St. Petersberg was stacked all of those years. If it was the NHL they'd be in major cap trouble.