Comprehensible input doesn’t mean that the input must be comprehensible in every of its detail. An optimal input is one that is still comprehensible even if there is a little noise or some incomprehensible pieces in it.
Therefore, we don’t need to understand 100% of the story. We don’t need to understand the complete meaning of each unfamiliar vocabulary or grammar, because every time we encounter a new word or a new structure in a comprehensible context, we will still be able to “feel” and acquire some sense of its meaning and use.
If we are exposed to enough meaningful stories (conversations and language-rich activities), and the stories are reasonably comprehensible, our brain will construct the meaning and usage of the words and the structure, and gradually substantial vocabulary and grammatical growth must take place.
And if the input is actually compelling, we might not even notice that there is noise. The noise fades into the background as we delegate the processing of that noise to our background intuition.
Several studies have compared the impact of hearing unfamiliar vocabulary and grammar in the context of a compelling story, helped by “comprehension-aiding supplementation,” with the traditional direct teaching of grammar and vocabulary. The consistent conclusion is that the former is more efficient: hearing unfamiliar words in the context of compelling stories results in more acquisition per minute.
So the time is better spent for more great stories, meaningful conversations and language-rich activities around it, in order to substantially grow language competence.