What you have written above pinpoints the reason I believe AL would be better suited as a legislator. In her home state, there is a moritorium on the DP and many people that feel the same way she does. In tandem with the people of Illinois, she can address "it" (the law) effectively. Many in Illinois do not wish to kill criminals and have set that forth in their laws by allowing a governor, elected by the people, to enact a moritorium.
However, as a lawyer, she can bring her viewpoint to other states. This shows a great committment to her cause, but at the same time, it is not lost on the people of Florida that this is really an assault on them and their laws. I think AL despises the DP so much that she, deep down inside, does question the culture of Floridians. But as an attorney defendnig a Floridian, she may have to choose her words more wisely, hence throwing the responsibility on the prosecution themselves.
ETA: And I do agree with JBean in this sense: The state does want to kill Casey, but they are elected officials, so they presumably are carrying out the will of the people, in order to be re-elected-Ah, politics!