Headcanon but also sorta theory?
The Nightmares were always Michael's. They're from his guilt. He tried a dream journal to understand what was up with them. Drawing what he saw. It varies from introspection like "I am feeling what he felt because of me. My favorite spot to scare him was the closet. We never left him alone." To simple entries like "I lost".
William definitely looked in there to see Mike's drawings and that since they are in a way partially a perspective of the fear his youngest son felt, it was perfect for these weird observation chambers.
Whether Michael actually went in those or not I think it definitely has angst potential with the invasion of privacy and the fact his own personal torment got forced onto other kids.