I think youre missing a key point on injuries. They happen to every team. Every last one. Do some teams experience more than others? Yes. But regardless, every team knows going into the season their preferred 9 man roster will be subject to personnel challenges over a 162 game season. Its a given.
So, there are two man ways to cope. The first is to invest in your training and conditioning staff. That makes players both less less likely to get injured, and more able to recover promptly when injured. Good coaching on the basics like proper sliding, ensuring extensive stretching and such can also reduce injuries, though not eliminate.
The other way is to have a deep bench, both at the major and minor level. A single dimensional team that has an excellent starting nine but lacks depoth will not make it through a complete season. Teams have to have more than adequate back ups, or procure them as necessary. The former is ideal because the latter can force trades that are not beneficial long term.
The bottom line is, over time, every team will see its fair share of good and bad luck in the injury dept. The best teams will incorporate practices and strategies that both limit injuries, to the degree possible, and have ready, adequate replacements when they inevitably occur. Those are the teams that will be regularly competitive for championships.
If a team lives on the backs of a few key players, without doing both of the things above, they are not liklkey to have the stamina to be successful for the long season.