Great question, Andy! This dialogue tactic helps to focus the conversation so that both the pro-life and pro-choice person are in a collaborative discussion about what the laws surrounding abortion should be, not just what they are right now or have been in the past. This setup is pretty open-ended so it may lead to any number of places, but the reason it is helpful is that the place you land will be customized for the specific person you're talking to. We believe different people need to hear different arguments, depending on what is most important to them. The benevolent dictator operates as a diagnostic tool because while the person is trying to think through the problem from this angle, they may decide that they would allow abortions in X circumstance, but not Y circumstance. Or perhaps they will allow abortion at a certain gestational age, but not another. Always ask them to explain why. While they explain why they would make the ruling in that way, you will often be able to identify the root of what is driving their pro-choice position.
Finding that rooting principle or argument that someone holds can be really difficult during a conversation because there is just so much stuff happening at once. This tool is designed to solve that problem. The rooting principle you identify can be different from one person to the next. Examples of this could be, but are not limited to: A) the unborn child is not a person with the same value as you or I B) your pro-choice friend thinks abortion should be used to prevent future suffering of that child C) they believe a woman's right to bodily autonomy justifies killing the human fetus. Once you and your friend find that underlying disagreement you have, the conversation should be much more linear and productive than before. You can give them an argument that refutes their rooting principle.