How do we know it isn't safe for the players? Do we know the line in terms of safe/unsafe between the number of games in a week/month?
I am generally interested in the science behind it, not trying to start anything.
I think it has to do with lack of recovery time. I'm pretty sure numerous studies have shown that recovery time post physical activity is very important, it's why you don't workout the same muscles in the gym everyday. After physical exertion, the muscles have these micro-tears that heal back "stronger". It's basically how you build bigger muscles. If you never give a chance to these micro-tears to heal, muscle fatigue sets in and the muscles can't perform as optimally as the usually do. Obviously, anyone who had a prior injury becomes at a greater risk of re-aggravating that injury, for others, a weakened muscle offers less protection to the joints and makes them more likely to be over-extended/torn.
I'm guessing sleep schedules will also be messed up with frequent overnight travel, if you're more tired, you're less sharp and alert and more likely to get injured during a play in a high paced sport like hockey.
All that said, these a pro-athletes getting paid an absurd amount of money to play hockey, they should be focused 100% on health and recovery during the season.