Injuries are fine as long as they're not too crazy. Yeah, in real life, players can get season-ending (even career-ending) injuries... but I hate games that take it that far... minor injuries are fine though and shake the game up a bit.
It is harder to gracefully pull off in a game that has training each week and you have to play to grow any. Injuries tend to be easier to swallow in a game where your players' playing time doesn't affect their growth (such as some baseball sims I've seen). Another issue is how short the seasons are (compared to the 82-game NBA seasons for example) so every week really counts so much more.
Still, I can take a guy missing 1-2 weeks in a season. I don't find that too extreme to be discouraging at all.