I played a few years (flag through high school varsity, no college) and I can remember always being encouraged to hit as hard as possible in practice, "practice how you play".
Coaches would always ask after a collision and somebody comes up lame, "are you hurt, or are you injured?". The implicated was, if your hurt, shake it off and get back in there. If you are injured go to the sideline and get medical attention because you are out, until you are medically cleared again.
So we were definitely trying to "hurt" each other, but never "injure"