This is why guys like Kahun washed out of the league while other guys like Sheary stayed. The thing that made Sheary stay in the NHL is that he went from an undersized, offensive winger to a 2-way winger that also PKed and could play in moderate defensive usage. Had he not had that development, Sheary would have been out of the NHL 5 years ago. People here complain about Sullivan insisting on guys like McGroarty and Poulin needing to PK and be defensively strong, but being able to PK and be defensively strong is what will actually allow them to stay in the league. Poulin is especially a guy that is trending towards that "good but not great and not specialized" group.
If you have 2 players competing for a 4th line PKing role, where one is a bad 5v5 player but has immense PKing experience and the other is a good 5v5 player but has no PKing experience, every coach is going to pick the first player. I'm not one to act like PKing is some sort of ultra special skill, but there are some guys who have been doing it since literally juniors and being specialized 4th line guys is what made them make the NHL. Puljujarvi has 11 career minutes on the PK in the NHL and I severely doubt he ever PKed much at all in the AHL, Liiga or juniors either. I don't think any team would bother trying to turn Puljujarvi into a PKer, especially when he's 26 already.
If he's to make it in the NHL, it's as a scoring 3rd liner that can drive play on a 2-way 3rd line. He doesn't have the track record for coaches to be patient with him, and he can't have runs of 3 points in 15 games early in a season if he wants to convince a coach he can be a regular in that kind of role. It's the same thought as when Sullivan said "Puustinen needs to score goals if he wants to play".