That is true only for the last c. 6K years, which, ironically, coincides with advent of recorded history. For example, Piraha have no concept of time and no creation myth (from a different angle their myth is simply that everything was as is when they popped up in their part of forest) and Australian Aborigines have "dreamtime" where myth exists, but past, present, and future happen all now (plus Aboriginal myths very closely correspond with bush and serve as a navigation tool via deliberate pareidolia as mnemotechnical device).

Since those cultures are what could be considered the last remnants of original animism (or the least influenced), there is a huge probability that it was the norm during prehistory and civilizations before Sumer (and in animistic societies / civilizations that continued to exists alongside it until c. 2000 BCE). You may argue than Pygmies, too, would fit the bill, but, while their myths are similar in function to Aboriginal ones, many aspects of Pigmy life come from neighboring tribes which enslaved/enslave them and which already entertain (poly)theistic mythology.

I think the main problem with myth is that it can become dogmatic and speculative (latter of which is, technically, the case of all philosophy, too).

https://senderspike.medium.com/modern-mythology-52498801ab24