Well, if next were an adjective it would need something to modify; e.g., the next person, and even if it were separated linearly from its noun, it would still have to modify that noun because adjectives can't stand alone:adjective: Sam is happy.
adjective: Sam is sad.
adjective: Sam is next.
Semantics alone tells us that next can't be an adjective; that it isn't nominal--that it doesn't modify a noun, which is the very reason it can't be a subject complement. Semantics.