The question concerns the observation that the floating quantifier prefers to immediately follow rather than immediately precede an auxiliary verb. Interestingly, however, the quantifier can readily immediately precede a content verb. Observe the following triplets:
(1a) ?The girls all have been trying hard.
(1b) The girls have all been trying hard.
(1c) The girls all tried hard.
(2a) ?My friends all can take time off work.
(2b) My friends can all take off work.
(2c) My friends all took time off work.
(3a) ?His answers all are written in two minutes.
(3b) His answers are all written in two minutes.
(3c) His answers all make no sense.
These sentences can easily be tested. If you read one of the a-sentences to an informant and ask him or her to repeat it, they inevitably repeat it as the b-version. They correct the position of the floating quantifier, and they often do so unknowingly. Note that the preference for the b-versions is strong enough that more is involved than just stylistic preferences, contrary to what Greg Lee writes.
Turning to the exact nature of the question, the assumption about adjunction to DP/NP may be incorrect. The fact that the c-examples above are perfectly good indicates that one has to acknowledge what immediately follows the floating quantifier. Thus, the question might be formulated more appropriately as follows:
Why can a floating quantifier only marginally immediately precede an auxiliary verb?
The answer to this question likely has to do with prosodic factors. Floating quantifiers prefer to immediately follow a prosodically weak word if one is present. Auxiliary verbs are prosodically weak.
Support for this explanation is seen in the following examples
(4a) I will eat all the chips.
(4b) *I will eat the chips all.
(4c) *I will eat all them.
(4d) I will eat them all.
If we assume that the quantifier can immediately precede prosodically strong expressions or immediately follow prosodically weak ones, then these data are predictable. The pronoun them is prosodically weak compared to the noun phrase the chips.
Further support for the insight that prosodic prominence is relevant to the distribution of floating quantifiers comes with the observation that the a-examples above improve if the subject NP is changed to a pronoun:
(1a') You all have been trying hard.
(2a') We all can take time off work.
(3a') They all are written in two minutes.
Corpus searches reveal that when floating all does in fact immediately precede an auxiliary verb, it does so only in the event that the subject is a prosodically weak pronoun.
I explore the phenomenon much more extensively in the conference proceedings here. The account I develop is couched in a dependency grammar framework of syntax.
As a final comment, the movement approach to accounting for the distribution of quantifiers is in my view on the wrong track. If I am right that it is, rather, prosodic factors that are important, then all the talk of movement with or without the quantifier is poppycock.