Alexander, like everything in Campaign, is used as a tool, a metaphor or an archetype, to challenge the reader to question the nature of life, existence and being. His role in the book is to be an example against whom all human fears and failings might be judged. Campaign is certainly a book that examines human fears and failings. Outside, the universe has been vanquished. It simply doesn't exist.
Decades pass in limitless corridors of locked doors and no escape.
Inside is contemplation, outside is nothing. Everything is white, sterile and clean, and the white doesn't want the travelers to leave. Ian and Barbara have both witnessed the death of the other and can't understand how they are still there. Ian falls into madness and kills the Doctor, again and again, broken with a blood as red as humanity, only to be reborn with a new face time after time. Susan attacks Ian verbally, berating him for a decade of self-pity when she and her Grandfather have seen, and thus lost, so much more than he can imagine.