Why is it "time of day" but "hour of the day"?

Well, the title is a little misleading, because both "time of day" and "time of the day" are possible and can have the same meaning.^[here] But "time of day" is more commonly used (when we're not mentioning a particular day, of course):

So you're more likely to hear:

We love to eat around this time of day.

But after we substitute "hour" for "time", the article is almost always in there:

So the previous example would become:

We love to eat around this hour of the day.

I imagine that native speakers of English would agree that it sounds a little off (or at least less natural) to say: ^?We love to eat around this hour of day.

These 2-grams† bellow will show that the tendency to omit the definite article after time of exists in other similar phrases too:

• Month of the year is used with the, whereas time of year is more commonly used without.
• Day of month is comparatively rare, but time of month can be acceptable.

† _{or bigrams, or n-grams, if you will}

To complicate things further, take a look at this 2-gram, which tells you that any time of the day is a little more common than any time of day; i.e., adding any kinda swaps the results around!
I guess this is because you're more likely to talk about a nonspecific time of a specific day, than to talk about any time of any day, for there is not much to say about it; hence the definite article before day.

I think that the difference is simply that "time" is not specific, whereas "hour", "day" or "month" refer to fixed amounts of time.

So time of day/month/year is a more general expression and "day of the year" or "hour of the day" are more specific, despite being sometimes used interchangeably as in "time of day" and "hour of the day".

Example :

This time of year gets very rainy / This month of the year gets 150cm of rain on average

I get sleepy this time of day / I like to take my medication at this hour of the day.