Some fans like to believe that Kadri taking so long to solidify himself in the NHL isn't natural, but it is. Many players have gone through similar development patterns and have gone on to have success in the NHL.
The following is a list of former first round draft picks who have taken at least three years before solidifying themselves as regular NHL players:
Bobby Ryan, T.J. Oshie, Steve Downie
Michael Grabner, Claude Giroux, Chris Stewart, Kyle Okposo
Lars Eller, Ryan McDonagh, Max Pacioretty, Kevin Shattenkirk, Logan Couture, James van Riemsdyk
Jake Gardiner, Cody Hodgson
2009 (Most likely players aside from Kadri)
Chris Kreider, Ryan Ellis, Carter Ashton, Louis Leblanc
Aside from the players mentioned in 2008 and 2009, all of the other players have managed to become regular NHL players. I could bore everyone with the details of each player but nobody wants to go through all that. However, each one of these players were up and down for at least the first three years after they were drafted. The most notable players on this list are Bobby Ryan, T.J. Oshie, Claude Giroux, Chris Stewart, Max Paccioretty, Logan Couture and, of course, James van Riemsdyk.
An interesting thing I noticed when researching this part was that current players in the Leafs system like Jake Gardiner and Carter Ashton are going down the same road as Nazem Kadri. Gardiner was drafted back in 2008 but did not make his mark until this past season—three years later. Carter Ashton was drafted back in 2009 along with Kadri and has yet to make his mark.
Progression is not a linear line. Everyone develops at their own pace. I understand it's natural to get frustrated when a player takes longer than expected, especially in a hockey hot bed like Toronto. However, many players have gone through exactly the same thing and have gone on to have success. There was a reason Kadri was drafted 7th overall, and I think it would be foolish to give up on that kind of potential so soon.