Whether Bowie was a true musical and compositional genius is debatable. I am currently half way through reading The Man Who Sold The World, which is a dissection of all Bowie's songs of the 1970s. In truth, it's a bit of an overly-serious slog but parts of it confirm my suspicion that in the early days at least, Bowie wrote his music as much by dictation to his musicians as by direct composition.
Be that as it may (or may not) where he truly excelled was at gathering the best musicians for the job, giving them just the right amount of direction, and then letting them do what they do. There are few better examples of this than Mike Garson's piano on Aladdin Sane.
The song is dark and disturbing enough already, but the two piano solos probably give a better description of mental instability than the words ever could.
Instead, the words focus on the humanity of madness. For all his demons, Aladdin is human and he needs to be loved, just like everybody else does. Although the lyrics are written in a mix of the third and second person, it's never made clear whether the song is about a character or whether the actor is referring to himself in the third person.
As the band fades out, the piano is left getting even darker, using both extremes of the keyboard before hanging on a dissonant chord, and finally an almost comical flourish to tell you things are going to be okay. That wasn't Bowie's doing per se, but he knew enough to give Garson his head and let him do exactly what the song needed.
Bowie's musicians appreciated the trust and space they were given and responded accordingly. Here is an amazing live version Mike Garson posted not long ago: