NPs can function as adverbials as in the following sentences:
I ran a mile. I am 5 feet tall.
One way to confirm this is by substituting the NPs with adverbs, e.g. "I ran fast" and "I am very tall". "A mile" in the first sentence may seem like the object of a transitive verb, but it isn't as how passivisation proves:
*A mile was run by me.
This, therefore, means that "run" is an intransitive verb with an adverbial, which is "a mile", an NP.
In the second sentence, "tall" is obviously an adjective that functions as the subject complement. This is confirmed by the use of copula "am", an intensive verb.
The problem comes when one tries to parse such adverbials in phrase structure form.
Can NP appear on the left branch as the sister of Adj (denoting premodification of Adj) as how an AdvP can?
E.g.: [AP [AdvP [Adv very]][Adj tall]] [AP [NP [Det 5][N feet]][Adj tall]]
Drawing [NP [Det 5][N' [N feet][AP [Adj tall]]]] must be out of the question as "tall" should be the one premodified, not "5 feet".
I've drawn this so far. 'X' is the anomalous part in question.