Think he needs a bigger role to ever be a good fit. It is just a different job description between (a) a role where you have to do as much as possible with little to work with and (b) be someone that plays with the puck on his stick on the PP, on a scoring line with more regular ice time, and so forth.
He can definitely take steps on a 3rd or 4th line, but if we are waiting for him to set the world on fire 5 on 5 in a smaller role we are waiting in vain. But that doesn't mean that he couldn't break out -- if he improved as much as he can and also gets a bigger role. Kakko is 23, history is full of examples of players who had done very little at the age of 23, in leagues below the NHL, that then break out later on.
What I think is the most problematic is that while Kakko of course has a lot of natural talent, there is always a risk that if a player like him plays in a smaller role for several years, when they get a shot in a bigger role they are not just prepared to take it on, while another 24 y/o who had played outside of the NHL running a PP every game might be able to do it better.