Why are location words like "here" adverbs rather than adjectives?

As John Lawler said in the answer to the first-linked question, calling “here” an adverb is not actually very useful for understanding how it functions in English.

In fact, there is more similarity between the behavior of here, home, at the park than there is between the behavior of here, carefully, very, despite the fact that conventional part of speech categorization calls carefully and very adverbs also.

Because here behaves similarly to prepositional phrases like at the park, it can be analyzed as belonging to the same part of speech as prepositions. This makes “preposition” a misnomer for the category (since “here” is not proposed to anything), but the Cambridge Grammar of the English Language uses preposition as the label for the set of location-describing words that encompasses traditional prepositions despite the mismatch with the term’s etymology.

It’s hard to explain why languages make the language-specific categorizations and generalizations that they do. You can say that it is because of analogies between words with similar meanings, but clearly the same analogies have not applied in all languages.

There are similarities in behavior between prepositional phrases (in the CGEL sense) and adjective phrases, but also differences. Both can be used as predicates or to modify nominal phrases. But prepositional phrases generally cannot be placed in the pre-nominal attributive position: we can say the blue house but not *the here house. This test shows that early and late exist as adjectives.

As far as "type of word", semantically, "here" is an adverb. An adverb's primary function is to qualify a verb.

We will play here tomorrow.

Syntactically, i.e., as far as what function it fulfills in the sentence, "here" can be:

1 - A "circumstantial complement of place".

Complements of time are a part of the sentence's predicate that qualifies the predicate's nucleus, (which is normally a verb), place-wise.

For example, in the sentence above, We will play here tomorrow.:

• "We" is the subject
• "will play here tomorrow" is the predicate, and within the predicate:
  • "will play" is the verbal nucleus
  • "here" is a circumstantial complement of place
  • "tomorrow" is a circumstantial complement of time

"Circumstantial complement" is not the only function that an adverbs can fulfill (although it is the most important).

2 - An attribute (qualifier) of an adjective (or attribute construction)

The insects present here belong to a new species.

In the above example:

• "belong to a new species" is the predicate
• "The insects present here" is the subject, and within the subject
  • "insects" is the nominal nucleus
  • "the" is an attribute (of the nucleus)
  • "present here" is an attribute (of the nucleus), and inside it:
    • "present" is the nucleus (of that adjectival construction)
    • "here" is an attribute (of "present")

3 - An attribute (qualifier) of another adverb (or circumstantial construction)

We resumed of operations starting here.

In the above example:

• "We" is the subject
• "resumed of operations starting here" is the predicate, and within it:
  • "resumed" is the verbal nucleus
    • "our operations" is a direct object
    • "starting here" is a circumstantial complement of mode (idicating how we are resuming)
      • "starting" is the (adverbial) nucleus of said construction
      • "here" is an attribute of "starting"

4 - A mandatory predicative

An exception of all the above is with copulative verbs, i.e. with verbs that have little meaning on their own and mandatorily need a complement.

In that case, whatever follows a copulative verb is by definition a "mandatory predicative", regardless of the type of word.

I am a good person.

He is here.

In the above examples, because "to be" is a copulative verb, both "a good person", and "here" are mandatory, subjective predicatives (despite being very different kinds of constructions, semantically speaking).