Tying monotheism to deserts is fine and valid (all regions where monotheism appeared saw the great desertification around 3000 BCE), but it still leaves a lot of inconsistencies unanswered.

1) No monotheism in Americas -- one would expect at least some form of it emerge in southwest of North America. Then again, all cultures with monotheism are also intimately tied to cannabis which was brought to "New World" only in 15th century CE. But still.

2) In Egypt the monotheism was but a very brief fad starting and ending with Akhenaten. This is pretty much in line with the overall observation that the common population, if left to its own devices, sticks to polytheism (see e.g. constant effort of Judaic authorities, mainly prophets, to keep the common folks "in line").

3) Esoteric/mystic core of all monotheistic religions (and I consider Vedic Hinduism with its concept of Brahman to be a form of monotheism too) is word for word identical. The actual form of the religion (creation myth, name of God, etc.) then heavily reflects the form of local polytheism.

Thus, you still have to explain why monotheism is always introduced from top to bottom (and does not naturally emerge from bottom as would be the case if it really evolved spontaneously in response to changing environment), and also why the core of all monotheistic religions is basically what we know as non-duality (and is like copy-paste all across the board).