I see what you're saying, but I have to push back on the Berggren comparison a bit. Zadina is a "offensive player" whose offensive skill isn't as good as people though. He's the offensive Brendan Smith (a "dyanmic" offensive player according to one LGW member). Berggren has the skill. His brain, passing, and skating are miles ahead of Filip. I'd argue his shot is too (his schot selection is better). The Red Wings really had two concerns about Berggren as best I can tell from what they've said publicly. First, that he's got to get to the inside of the ice more to score more goals. Second, that he's got to use his teammates more in transition. Both are valid. He's a bit of a puckhog in transition and prefers to sit on the outside and look for seam passes to open teammates. But both of those things can be attributed to the fact that he didn't play for basically two years. He lost massive developmental time (i.e. time with coaches telling him how to make adjustments).
The issue with Zadina isn't that he plays a perimeter game. The issue is that his skillset isn't as good as people thought. He's a MUCH worse shooter. He doesn't really play with speed. His playmaking is nonexistent. He's good for gaining the zone in transition but the minute he gets there he either A) throws the puck into traffic and turns it over, or B) plays catch with the goalie. He's completely lost in the offensive zone...which was supposed to be his bread and butter.
Berggren has no such issues. For him to be as good as he can be he's got to make small adjustments, but the skill he was drafted on is there. When he gains the zone he's immediately finding passing options and executing. His shot continues to improve but will never be his primary way of hurting you. Right now I'd say he's got Gustav Nyquist floor and Viktor Arvidsson ceiling. Both are perimeter players, but neither were ever seriously going to bust. Zadina, on the other hand, might very well be playing in the Swiss League in a few years.
Edit: Oh, I wanted to mention deception too. Zadina has ZERO deception in his game. He has tunnel vision. If he's gonna pass he watches the receiving player all the way. When he's gonna shoot he might as well yell to the goalie and let him know where the puck is going. He's so goddamn frustrating.