I think the sex scene would have taken away from the story because it would have made the mother/wife and Denzel's character much less sympathetic.
When would he have slept with her? Before the child gets kidnapped while she is married? Or after the child is kidnapped? I wouldn't have liked either he mom or Denzel if that had happoened.
So that might have been the reason for the decision more than any black-white issues. Sex being sex and all
And as far as cop roles for the black man, I thinkit might be that we are over burdened with cop roles in general. They just make it look to exciting to be a police officer . . all that drama and gun-play.
And because of which I have to deal with some cop walking up to my car with "shooters"glasses on and a hand on his gun to give me a ticket for a burned out tail light. They believe this stuff.