I just ran most of a season as the Arizona Diamondbacks. I stopped when I had compiled a dozen DTD injuries and yes, all of them had at least minimal influence on Hitting, Running, or Throwing. Maybe this is a design decision? Minimal is minimal, and if you have an arm injury, you still have to swing your arms when hitting and running.
This is a non-sequitur, but what bothered me in this exercise was running across this DTD injury. How can you have a 4-5 month DTD torn meniscus injury?