The team as constructed should be getting outhit. For better or worse, we don't have many players who are big time hitters. And that's fine because hitting is just one means to an end. The important thing is separating the puck from the attacking player. If you do that with your body or your stick, its all the same to me.
The problem with looking at hits in a vacuum is that a lot of the time players chase hits. They are getting out of position to finish a check, but aren't separating puck from player in doing so. You can be a half a second behind the play and still get a "hit" wihtout really doing much for your team. In fact, it can be a negative as a player can take himself out of the play trying to hit too. With a poke check, if done right, your body is generally between the puck and the net. If you miss the poke, you are still in position. Our D have long reach and are generally good with their stick, so that is preferable to hits for the sake of hits. Players should play to their strengths, not chase some arbitrary stat.
As an example, Nicklas Lidstrom, one of the best D of all time, had 212 hits over his last 5 years (since they starting tracking hits). That's an average of only 42 hits a year, or .53 hits a game. Compared to let's say, Zaitsev, who imo is a borderline NHL player. Zaitsev has 383 hits in his 2 and a half year career, for 1.94 hits per game. That's almost 4 times as much. Who would help a team win more? Prime Lidstrom and his hit every other game, or prime Zaitsev with his 2 hits a game? Or compare Bergeron, a multiple selke winner, and his .73/gm since they started tracking them vs Steve Ott and his over 3 hits/gm. Also when comparing these stats, Lidstrom and Bergeron because they are far superior players, also play more minutes than their comparison, so the hits per minute numbers are even more slanted.