I used to basically ignore this attribute, in favor of SPD and ELU. Then I somewhat accidentally ended up with a RB who surprised me and became a stud on my Wishbone team. He still had very good SPD and ELU, but his STR was way better than my other guys. I thought he would by my #3 or #4 but ended up starting for over 3 seasons and actually outperformed my #1 guy who was a 4 year stud/starter.
So...its really only one data point, but how much does STR really impact how a RB performs in this game?