Body checking and falls do not account for the concussion issues faced by the League.  The NHL makes exceptions on head shots for various circumstances and only punishes the most extreme.  That latitude gives players flexibility which means the core behaviour that drives concussions does not change.

Zero tolerance on head shots will solve the problem.  Players will learn over time although in the learning process, players will get suspended that are marginal infractions.  But it is the punishment of the marginal infractions that will change the overall behaviour that eliminates head shots.  That will make the game safe.

As Dryden correctly notes, the game without superfluous violence, head shots, and fighting is an exciting, engaging game that is fun to watch.