This line of thinking makes no sense whatsoever.
A 40 point player is essentially a 4+ million dollar paid NHLer at this point in time, and will only go up. This isn't 2010 anymore, 4-7 million is the going rate for 2nd line players, and Whites contract places him on the low end. White is 22, will improve, and is already a 5 million dollar NHLer, even if he just replicates his 0.58ppg he got in his rookie season. Then take into account he isn't just a scorer, and it's easy to see.
Turris contract was assuredly used as a benchmark by both the Sens and White's camp.
White's 4.75 x 6 and Turris's 3.5 x 6 come out to be the exact same % of total team cap, down to the 2nd decimal point, at 5.83%. This isn't a coincidence, and is a going rate for a low level 2nd, high level 3rd line center. They are the exact same deal, prorated by cap hit.