I have red packs in the hundreds but I consider 3~5 players constantly injured typical. If he's not out for 10 days or fast trainer or something I probably won't use packs.

Does upgrading grass lower the injury rate? Nobody knows, but it is a requirement for larger stadium and academy anyways...
As I could recall yes, the difference between level 0 and max grass is very significant, but players still get injured.

It's annoying but everybody have the same problem.