14 down vote +200 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”: