Actually there are practical moments as I see it.And also, something I've been wondering about, is Buddhist practice in the present at all affected by whichever side of this argument is correct, if either? I'm not trying to encourage that the issue be ignored, things like this should be investigated, but since as far as I can tell the training remains the same, it isn't quite such a big deal.
First... it concerns Right Views. One can think that Buddha didn't say that there is NO self, because he only listed not-self phenomena, and okey, let them be not-me, but there is still some very sublime type of ME and this is good. So this view about nibbanic consciousness can create this "sublime" self-view.
Second... even if we let go of all possible self-views (even transcendent ones), we may still keep clinging to consciousness as to something that "should not be annihilated". Of course, in our practise we'll have to let go of consciousness completely only on the higher stages - possibly - only when jhanas are well developed. And so one can say this is a too far point of practice. But this is a point where we can "stuck" still clining to consciousness, unable to let go because of that very idea, that consciousness should "be" in nibbana (or - that nibbana IS consciousness).
By the way, there is also a very interesting thing as nirodha-samapatti. It is said (probably only in commentaries) that there is no consciousness at all. In the suttas we often see this way of fermentation destruction - that is reaching nirodha-samapatti. As far as I understand, in this method one destroys delusion by seeing that actually "there is nothing left, and even consciousness has gone". Seeing it this way his ignorance is destroyed either completely or to the level of anagami. One sees: "Ow yes.. there is really no me, even "very hidden or very sublime".