There isn't much need for an explanation. The fringe theories are equating unrelated iconography and objects.

In Assyrian art, sages (Akkadian apkallū) are often depicted holding a "purifier" (Akk. mullilu, some sort of conifer cone) in the right hand and a "bucket" (Akk. banduddû) in the left hand. For example, one spell describes the magical figurines necessary for the ritual.

7 ṣalmē alpkallē ša ṭīdi pan iṣṣūri kappē šaknu ina qāti imittišunu millila ina qāti šumēlišunu GIŠ.BA.AN.DU8.DU8-ú našû

7 apkallu-figurines of clay, which have bird faces and wings. In their right hands they carry the purifier, in their left the bucket.

There are several [surviving examples](https://www.christies.com/img/LotImages/2012/CSK/2012_CSK_07207_0014_000(an_urartian_silver_situla_circa_9th_century_bc).jpg) of these ritual buckets. They are functionally the same as situlae from Egypt, Greece, Etruria, and elsewhere in the eastern Mediterranean and ancient Near East.

This sort of purificatory ritual has even survived to the current day in the form of the sprinkling of holy water in Catholic churches.

Other cited examples of the so-called "handbag" motif - such as the weights of the 3rd millennium BCE

• resemble the Assyrian buckets only due to the two-dimensionality of Assyrian art. It is rather like claiming that the Egyptian tree hieroglyph is the same motif as a spearhead.