Suzaku said from day 1 he is going to change the rules and people's minds by his actions. Just capturing her wouldn't do this. He clearly shows this by saying he would rather change her mind and people like her than kill her and others in battle fighting fire with fire. Suzaku is using Honey while Zero is using Vinegar. When he talks about systems and order he says he wants to change them but believes completely destroying them wouldn't work. Which IRL he is proven right in many cases when rebels take over and destroy established govs completely and become even more corrupt in the end.