We always predict as well we can - that's just how the brain works. Even without narration we'll be subconsciously comparing what we're seeing to past experiences and using those experiences to predict what comes next at various levels of abstraction.

I highly doubt we have any intrinsic bias towards perceiving things as following a story template, since our DNA has been shaped by nature, not stories. The major bias we do have, encoded in the way that our brain works, is just that nature is largely predictable on various scales - next time will be the same as last time - and this bias is what causes us to predict and perceive/segment current experience based on past experience.