Over the past few months, I have read numerous comments about the limitations of Woodson in his offensive scheme. I am certainly  skeptical about his critics after lookng at the team as it is structured.
First of all, all the Hawks starters except Joe have a significant offensive weakness. Marvin cannot post up or drive to the basket, Josh has no jump shot, Al low post moves are mechanical and are still developing and most importantly, Bibby does not have the speed to penetrate.
These glaring weaknesses severely limits the Hawks ability to run multiple offensive schemes. Teams do a lot of home work and know each players weaknesses. Hence, all they have to do is to give the player his least likely opportunity to score.
The key to winning in this league is to focus on your strength. The Hawks strength is clearly Joe at the 2 . Joe is taller, stronger and heavier that virtually all  2 guards in the league and also can score in multiple ways. This gives him a significant advantage over other 2 guards. So the Hawks best chance of scoring is simply to give the ball to Joe. Sometimes, the simplest solution  is the best solution. I have watched time and time again as the Hawks offense has grinded to a halt when Joe is not part of the offense, when they run a play that leaves other players open or when Joe is out of the game.
The Hawks are not like the Blazers,Magic or Boston  that have versatile bigs, penetrating point guards and multi skilled players . Hence, ther ability to run multiple offensive schemes right now is limited and   does not make any sense. Maybe in 2 or 3 years when hopefully these players have worked on their weaknesses and maybe Teague  is a starter, the Hawks can run a more sophisticated offense.
Right now, the Hawks best option in the half court  offense is simply to give the ball to Joe and have other players stand at a position that gives them a high percentage shot. If the opponent does not double team Joe( most teams for some reason do not), then Joe has to make a move to the basket.
To say that Woodson does not have the ability change the offense is not a fair statement. Even of he does not have the ability which I seriously  doubt, I am sure he has an offensive coach on the team that can implement it.
Hopefully with  the addition of Joe Smith and Jamal, the Hawks will have more options this season of running more offensive schemes.