I cannot understand why "would" cannot be interchanged with "can". Can SOMEONE please explain this? It is the difference between being WILLING to and being ABLE to. Both of which make sense.
Also... 'would' is a more polite (but often less used) way to ask someone to do something. Even though you are correct I don't believe it should be accepted here. Technically speaking 'would' is conditional. In Spanish it would be: Llevarías la caja a la cocina?
Even though I agree either could be used here in everyday speech, from a teaching perspective, it is also important to understand the conditional nature of 'would'. As a different tense the conjugation of the Spanish verb changes which is important to learn.