This seemed to be approach during the Haslett era--get the physically talented low character guys in FA and through the draft and build a Championship team. Names that come quickly to mind are: Albert Connell, Dale Carter, and draft picks like Talman Gardner and Adrian McPherson.
I'm not saying FA's and draft picks don't overcome previous troubles--look at Moss and Sapp. However, I would prefer to take my chances with high character guys like Duece, Brees, Pierre Thomas, Colston, Jhari Evans than roll the dice and revisit the Haslett era. Look only as far as the Bengals for perhaps the most physically talented team in the NFL as a prime example of the effect character issues have on winning.