Could someone explain why "We need to work during the day" was marked wrong. I understand why the unnamed pronoun "one" works here, but why don't the generalized expressions "you" and "we"? What is it about the Russian sentence that absolutely rules out the possibility or likelihood of the speaker meaning "you", "we" or even "I"?
In America, you would probably hear 'We need to work during the day'. We would also say 'We need to work in the morning' or 'Everyone should work during the day' or 'We should work during the day'. To say "one should" at the beginning of a sentence is way too formal for day-to-day situations in America.
A second question: Why is the sentence normative ("one should work", as if it is a moral imperative) as opposed to descriptive ("one must work during the day" because there simply aren't any night jobs)? What is it about this sentence's construction that converts надо from descriptive to normative? And if I wanted to articulate a descriptive statement of fact, "One must (as opposed to should) work during the day," would replacing надо with нужно make that intent clearer? Thank you in advance.
Your terminology is a bit confusing. "Nominative" is a case in grammar, both in Russian and English, confined mostly to subjects of sentences and predicates (things that modify or explain the subject), and what you seem to mean is something like "advisory": "One should..." gives advice, but it does not require anything. "One must..." is obligatory, because it obliges or requires one to do something.
Here's an explanation of the difference between надо и нужно:
Based on the explanation, the difference doesn't have anything to do with your concerns. With verbs, you can use надо/нужно interchangeably, as with работать, and both mean "need/must [perform the verb]". You never use надо with nouns, only нусно (not relevant here).
Based on the video, it would seem that the exercise means "During the day, one must work." Duo does not explain at all where "should work" comes from, because that is not what надо appears to mean.
I used a context search engine, and some on-line translators, and kept getting Надо/нужно работать for "should work" - but the context indicate that "should" was a kind of polite form of "must expect" or "need to expect" rather than leaving an option open to not performing the verb that followed. The sentences did not read like "You should do this thing, but you don't have to if you don't want to"; rather, they read like "You should expect to do this thing".
There's a difference between "You should go" and "As part of your job, you should go", because the latter indicates that you need to do something, and there will be consequences if you don't. You perhaps may not do what you need to do, but I just do not see надо/нужно as simply being suggestive or advisory, but rather advisory/obligatory. There's a fuzzy line of distinction there.