Actually for a one dimensional player, 3 shots in 5 games is not fine, 7 or 8 minutes a game or not. A good player just playing offensively should and would have more than that. My Prediction is Pulkks will be in Europe within 2-3 years. He doesn't do enough to play in the NHL, he just kind of floats around out there and gets random shots on net. He doesn't even look engaged in the play out there.
Imo, his biggest problem he never couldn't overcome was his short reach. He can't protect the puck, because he is small with shorts hands and short stick. Bigger players always steal or tip the puck off easily from his stick.
And for same reason, Pulkkinen is defensively useless. He can't steal pucks without a good reach. He is too small to steal pucks with hitting. Pavel Datsyuk had those ape-man hands, which did enable him to use longer stick than players with his actual height usually use. That longer stick and reach enables bigger puck control area = that's protection. Those ape-man hands made Pavel an ultimate weapon and a puck-thief.
Also, with small reach, Pulkkinen's shooting area is very small. You have to pass the puck in a perfect spot to get that one-timer off. Etc. etc.
Everything comes to that reach. Both offensive and defensive flaws. An that problem will never change against huge-reach NHL players in NHL-sized rink. But he will flourish at Europe, more space and not so protection-based hockey.