Strictly speaking, the allative (or lative) case denotes motion towards a location, and in this case not only "-en" but "-n" itself could be reanalyzed as allative. Grammatical markers, cases, declensions and conjunctions in languages often have different functions/names on a case by case basis. In English for example, the pronoun "me" in colloquial description is the objective form of "I" and can function as a "direct" or "indirect" object. Therefore the accusative in English can function as an objective, a dative, or an oblique.
Similarly, if we analyze deeply enough, we could place all kinds obtuse linguistic labels on the secondary functions of -n like allative/lative like in "iri ien", or temporal like in "ŝi iros lundon". However, the main difference seperating -n from these cases is that -n in itself is just the accusative. It is very flexible and multifunctional and may function sometimes like an allative or temporal marker, but in the end it remains the accusative. In the same vain, one would not be able to analyze -en words out of being adverbs.
These kinds of labels aren't really used in language learning (a field relevant to Esperanto, given that a good portion of it's speakers are learners) because they don't really have any pedagogical value. Most people don't have the linguistic background or interest to understand or be curious about the terminology. Putting emphasis on these formations could also give the false impression to learners that -en are as commonly used as a simple al la __ phrase.