This is an old narrative that doesn't apply anymore. We have been drafting some size the last few years and it's clear we have been adding size to the draft criteria. Average height in the NHL is 6.01 and the great majority of our picks in the last while are above that:
2016: Givani Smith (6.02, 209 lbs), Malmstrom (6.02), Sambrook (6.02), Larsson (6.02) Elfstrom (6.03) and no one under 6 ft.
2015: Svech (6.03, 205), Van Pottelberghe (6.02), Pearson (6.02), Holway (6.04, 201), only Saarijarvi (5.10) is under 6 ft.
2014: Larkin (6,01), Turgeon (6.02, 203), Ehn (6.02), Perry (6.03), Vahatalo (6.05), Kadeykin (6.05, 227 lbs) Holmstrom (is 6 ft, but 200 lbs)
2013: Mantha (6.05, 221), Nastasiuk (6.02, 202 lbs), Bertuzzi (6.01) Jarnmark (6.01), Pope (6.03), Wheaton (6.05, 223), McNutly (6.06, 210), Melen (6.02)
So. in the past 4 years, we've only taken 2 players that were 6 ft. or smaller (aka on the small side). That shows a clear choice for size.