At Night or In the Night?

The bottom line is “it’s idiomatic” as mentioned but I can offer the below rationale:

1. The origin of “at night” to indicate a point of time and the usage of prepositions “in” and”at”

In olden times, when the time expression “at night” was originated, night might have been thought as a point of time in the day because there wasn’t any activity going on and people were sleeping that time unlike daytime. It represents the dark hours and the late time of the day. But morning, afternoon and evening represent a period of time during the daytime where activities were going on.

In fact, night is a period like morning. This is the main reason of the question because the preposition in is used for time periods. Then, the question can be easily changed to “why not at morning but in the morning” because it seems like times within the day generally take at (at noon, at 5:00, at dawn, at dinner, at night), except the ones that take in with the definite article the (in the morning, in the evening, in the afternoon).

Speaking exceptions, one grammar book says the below for at under the title “exceptions: at, on and by”:

At can be used for periods identified vaguely, as in at that time, at breakfast time, at night; also for short holiday periods (at Christmas, at Easter). In BrE, at the weekend is used, but in AmE on the weekend.

A Communicative Grammar of English By Geoffrey Leech, Jan Svartvik

In the end, at and in share a long history for the usages that we talk about and it is mentioned as below in OED (including the earliest example and some relevant examples):

at, prep.
IV. Of time, order, occasion, cause, object.
29. Introducing the time at which an event happens:
a. with the time named.

• c1230 (▸?a1200)   Ancrene Riwle (Corpus Cambr.) (1962) 28 Ed al le þe oþre tiden.
• 1586    T. Bright Treat. Melancholie xviii. 114 From 3. at after noone till nine at night.
• a1616    Shakespeare Cymbeline (1623) i. iii. 32 At the sixt houre of Morne, at Noone, at Midnight.

in, prep.
III. Of time.
18.
a. Within the limits of a period or space of time.
With in the day, in the night: cf. by day, by night at by prep. 19b.

• a900    Anglo-Saxon Chron. ann. 709 In foreweardum Danieles dagum.
• 13..    K. Alis. 85 By cler candel, in the nyght.
• a1616    Shakespeare Two Gentlemen of Verona (1623) iii. i. 178 Except I be by Siluia in the night..Vnlesse I looke on Siluia in the day.

2. Chaucer’s influence on English and vernacular literature

One of the earliest usages of “at night” is from Chaucer’s works. However, there is one earlier usage listed in OED. The following are the definition of at night and earliest examples from OED:

at night: at nightfall, in the evening or night; during the hours of darkness. Freq. designating a specified time.

• c1300    St. Theophilus (Laud) 161 in C. Horstmann Early S.-Eng. Legendary (1887) 293 (MED), Þis cas bi-feol in leinte on a satures-day at niȝt.
• ▸c1387–95    Chaucer Canterbury Tales Prol. 23 At nyght was come..Wel nyne and twenty in a compaignye.

It seems like Chaucer might have a big role for the common usage of this idiomatic expression and the usage of this expression has been continued by other influential people like Shakespeare (example from OED):

a1616    Shakespeare Macbeth (1623) iii. i. 43 Let euery man be master of his time Till seuen at Night.

Additionally, the expression in the night has a long history as well and OED lists as below: (including the earliest example and some relevant examples)

b. in (also †of, †on, †upon) the night : by night, during the night.

• OE    Old Eng. Hexateuch: Exod. (Claud.) xii. 12 Ic fare on ðære nihte ofer eall Egypta land.
• a1400 (▸a1325)    Cursor Mundi (Vesp.) 6196 Drightin self þam ledd þair wai… Wit firen piler on þe night [c1460 Laud vpon the nyȝt].
• c1480 (▸a1400)    St. Theodora 288 in W. M. Metcalfe Legends Saints Sc. Dial. (1896)   II. 107 To þat thing has he na sycht þat thocht or don is in þe nycht.
• 1600    Shakespeare Midsummer Night’s Dream ii. i. 253 There sleepes Tytania, sometime of the night.
• 1990    N.Y. Mag. 30 Apr. 52/1 A dog howling in the night.

On the other hand, there are instances of at morning, at evening and at afternoon but they are uncommon and literary mainly. (See: Ngram result)

OED mentions the below adverbial phrases with modifying preposition (without article) for morning:

at (also †in, †on, before, till, etc.) morning , from morning till evening, from morning to night, etc. Also with adjective, as all (also each, every, next, etc.) morning. Cf. a-morning adv.

There are examples with at morning and at evening and the earliest usage mentioned is in morning. The below are first three earliest usages and some relevant examples from OED:

• a1400 (▸a1325)    Cursor Mundi (Vesp.) 7181 On nighter-tale, or in morning.
• c1400 (▸?a1387)    Langland Piers Plowman (Huntington HM 137) (1873) C. xiv. 147 (MED), Maules drowen hem to maules on morwenynge by hem-self, And femeles to femeles.
• c1475 (▸a1449)    Lydgate Testament (Harl. 218) 286 in Minor Poems (1911) i. 340 Thamerous foules with motytes and carolles, Salue this sesoun euery morwenyng.
• 1679    Processes Kirkcudbright Sheriff Court No. 282 Otherwayes no master that hath ane servant at night is sure to have them at morning.
• 1849    M. Arnold New Sirens i, I, who in your train at morning Stroll’d and sang with joyful mind, Heard, at evening, sounds of warning.
• 1968    D. Moraes My Son’s Father i. 3 At morning the sea was a very pale, indolent colour.

Finally, I’m including the below explanation from a linguistics standpoint (from the book Cognitive and Communicative Approaches to Linguistic Analysis edited by Ellen Contini-Morava, Robert S. Kirsner, Betsy Rodriguez-Bachiller). In summary, night is an exception and is shrunk to a point as a contrastive location in time in the phrase at night and the difference between at night and in the night is explained with examples.

At for temporal messages

…at, designating a point in space, is used for point in time as well:

   (37) He arrived at three o’clock; at noon; at midnight; at sunset; at dawn.

Just as a spatial point has no length, depth, or height, a temporal point such as three o’clock and noon, has no duration. A problematic use of at is the phrase at night. Unlike noon, night lasts from eight to twelve hours. Section 3 showed that a three-dimensional location is sometimes shrunk to a point when the message is one of contrastive location. At night is the temporal analog of at Plattsburgh and at Stoneybrook, contrastive location in time:

   (38) What do the pretty SMU girls like on their plates?
         “Pretty much hamburger, hotdogs, steak and, at night, maybe pizza”   Brown, 70361

The contrast in (38) is the different food preferences of the girls at the noon and evening meals. The implication of contrast in at night is better perceived when compared to in the night. Suppose the song ‘Strangers in the Night’ were titles ‘Strangers at night’. The title would no longer suggest two lonely people searching each other out, but a dysfunctional couple: “Companions by Day, Strangers at Night”.

In example (39), the two phrases appear in a single passage. The neighbor of a woman who may or may not have committed suicide describes the circumstances of her death:

   (39) I had made a habit of calling her at night, from my cottage, just to check. The last night I had called, but the line as always busy and it reassured me…
   She was found the day after at the bottom of the cliff. I tried to believe that what must have happened was that, restless, disturbed by this telephone call or whatever, she walked out in the night, as she had a habit of doing…With all that warm rain an the fog it might have been as simple as a loosened rock, a misstep.   Brown,1171886

The phrase at night implies ‘evenings rather than daytime’ for the regular calls, a message of temporal contrast. In the night carries no hint of contrast; it describes the dark three-dimensional space into which the woman walked.