Is the usage of “night and day” as “completely different” very common?

Solution 1:

Yes, it is very common. We (US) say, like night and day to indicate opposites. Google "like night and day" and you'll see the option for idiom. completely different:

On snooping disclosures, AT&T and Internet companies are like night and day. -pcworld
Bar Sue and the London Plane Are Like Night and Day: Two Reviews -DC newspaper

Interestingly, "like night and day" gave me hits for many of the dictionaries you listed.

The spokesperson used the idiom abnormally, truncated into an adjective form, instead of as the simile it is.

Solution 2:

Night & Day is similarly used to "black and white" therefore opposites. Implying a preference for one or the other and therefore an improvement is not common usage.

Solution 3:

Working day and night, is literal....possibly an exaggeration, but literal, describing a lot of time working. But when night and day are used in comparison to each other, it is metaphoric and means extreme difference, polar opposites, black and white..etc.