A system of chanting for memory has been used since pre-history across many cultures. See for example Greek epic poetry, Hebrew Scripture, Arabic Koran, Anglo-Saxon Beowulf, Viking sagas.
In ptr-literate societies, bards were able to memorize huge amounts of information and recite to their listeners. Much of the poetry with its rhyme/meter/repetition was written that way to aid in memorization.
That sort of memorization got a lot less as literacy grew and people could just read stuff for themselves, but it was pretty widespread and certainly not something unique to the Vedic tradition.