Would it be possible to remove the injury possibility from the foul fest that happens at the end of close games? It makes no sense that someone could be injured by the soft fouls that put someone at the line.
BB is based on reality (but it isn't perfect), so I am about 99.9% sure that BBs wouldn't change this. Injuries can and will happen at any time, just like in real life. With that said, there is not much, if anything, that can be done about it. I understand your frustration as I have had and still have my fair share of injuries.
If this is not possible then every foul under one minute should be an intentional or flagrant foul.
In my opinion, this would be ridiculous and very unrealistic. In real life, not every foul that happens under 1 minute is a flagrant or even a hard foul. The same thing goes with intentional fouls under a minute. Take, for example, a team that is blowing out the other team, but commits a foul. Chances are that it wasn't intentional.
Hope this answered your question.