Thinking about both the Abrahamic religions and others here - eg the concept of Brahman in Hinduism, Zoroastrianism, maybe some aspects of Buddhism, Atenism etc. in contrast to religions such as Jainism, various kinds of paganism and folk religions, and others which are surviving polytheistic religions but which lack that integration into state structures monotheism seems able to achieve.
To me it seems fairly intuitive that a consolidating state would seek to derive a unique legitimacy from a unique supreme being, but I'd be interested to hear if this is a subject historians have written about.
This is probably too much of a "throughout history" or speculative question. If you specify down to a specific religious era or region (such as Zoroastrianism and the Persian state), we should be better able to answer your question.