Why did oral storytelling traditions favor strong meter and alliteration?

Because scops (oral storytellers) were telling their stories orally and not from a written account, they needed something that would allow them to easily remember those stories. This why you notice that tales or epics that were first told orally have a certain cadence that makes it easier to follow. This allows the storyteller to remember and it also allows the reader to follow along in a better way.

As an interesting side note, these story tellers would also sometimes put the stories to music as that was another way to tell the stories. They would start as ballads and the storyteller would play a tune while they sang the stories.