FOOD FOR THOUGHT: Let's get a meaty discussion going. 
But not a subject complement, right? Because those are nominal, and which leads to this question: why can't
next be a preposition here,
Who is next? (aside from what's obvious: it doesn't have an object, but particle prepositions can occur without an object in phrasal verbs, right? They're often called adverbial in that position, though, to account for it.)
That is, non-linking forms of the verb BE take adverbs in the predicate, but the form and function of those adverbs aren't always the same. For example,
She's in the house.
Form: prepositional phrase <nominal>
Function: adverbial <tells us where>
So, given that adverbs give off this kind of duality,
[I'm not sure what you mean here by duality.]why couldn't
next in
Who's next? be a preposition in form
[I think form (or construction) and function (or usage) are not mutually exclusive or need belong to the same part of speech. Form or construction does not have anything to do with being a part of speech. For example, a preposition phrase (classification by construction) is thus called because it starts with (is headed by) a preposition, but functionally (classification by usage) it may be used as a noun phrase, an adjective phrase, or an adverb phrase.] that is, be nominal and thereby privy to the category "subject complement"? Why is it called a predicate adverb?
In short, why does the verb BE have to be split into linking and non-linking kinds?
I thought BE is always a linking verb, there is no two kinds.
What's the difference in meaning here?
Adverb: The person is
next => Adjective: the
next person
Adjective: the
next person => Adverb: The person is
next.