Adam, I think you are missing the bigger picture here. The point of reading aloud is to hear fluency, thereby creating new fluency memories that wash out the stuttering memories. In Lee’s book, he speaks about the MMIB.
We need to replace all the negative stuttering memories with fluency memories, and how better to do it than when reading aloud alone, under no pressure, with nobody listening or grading you. It is the perfect place to practice fluency as you are calm and you can go at your own pace.
Many PWS can read aloud alone without stuttering, with a very few exceptions (and even they can read aloud alone if they whisper). Eventually, your brain would have heard so much fluency from reading aloud, that it will forget to stutter. This will then lead to fluent conversations with people, as your brain has now formed the habit of fluency.
Hope this helps!