Where is "allí"?

According to traditional grammarians “allí” (here) is an adverb (some times is called a “pronominal adverb”). That is not so clear. It is true that it has a locative meaning, but this is not evidence that it is an adverb. It cannot be an adverb because it can modify a noun:

(1) Las andanzas de Juan Pérez allí
(2) Su discurso allí

It is important to confirm that in these noun phrases “allí” is inside the NP. We can check this if we include them in a sentence:

(3) Me importan un bledo las andanzas de Juan Pérez allí
(4) Me importa un bledo su discurso allí

Notice that in these sentences “allí” does not modify the verb. We cannot extract “allí” out of the NP:

(5) * [Allí] me importan un bledo [las andanzas de Juan Pérez __ ]
(6) * [Allí] me importa un bledo [su discurso __ ]

Correspondingly, we cannot extract the locative PP that “allí” is replacing:

(7) * [En Salamanca] me importan un bledo [las andanzas de Juan Pérez __ ]
(8) * [En Salamanca] me importa un bledo [su discurso __ ]

Notice, also, that “allí” can modify a verb in other cases:

(9) Vi a Pedro allí
(10) Pintó el cuadro allí

As expected, in these cases, “allí” can be extracted:

(11) Allí vi a Pedro
(12) Allí pintó el cuadro

This lead to some potential ambiguity with some verbs:

(13) Me enteré de las andanzas de Juan Pérez allí
(14) Oí su discurso allí

In these cases, “allí” modifies the verb or the noun, and it can only be extracted in the first possibility (when it modifies the verb).

Does this mean that “allí” is a pronoun in ablative case? What about "acá", "aquí", and other similar to them (which behave similarly)?