Translation:Nhà của tôi
While I understand that the use of "ngoi" is not necessary for the sentence to be intelligable, the point I'm making is that it would be more logical to enforce its use on this occasion as the topic of the lesson is regarding classifers.
For example, if the use of "ngoi" was enforced in this question, and the student omits it and gets it wrong, it would be a reminder to them of the classifier.
With things as they presently are, if you just permit them to answer without the classifier, then what have they learnt about the classifer? Nothing.
So if brevity is more persuasive, I'd say:
It's not necessary, but more logical.
I think the problem with your suggestion is that these exercises can appear also during the generic training. One would thus have to remember that in some particular cases some specific things are enforced even if not actually required by the language. This can get frustrating quite easily in my opinion.
I suppose it is, at the cost of not teaching the classifiers for nhà.
Is that a worthwhile cost? I leave that up to the course organisers.
Was the perspective you mention their intention when they devised this question+answer? I suspect not. I suspect it was more of an oversight, one worth pointing out with the feedback given.