The first article in this blog post series has a little section talking briefly about this history, and there's a representation of this that I think sheds a lot of light on the original design. See the heading "Side-Note on Month / Day Determination" in the below link [1].

Displaying the months like the following helps see the regularity at a glance. Columns 1, 3 and 5 are the long months, others being shorter:

  +-----+-----+-----+-----+-----+
  | 31  | 30  | 31  | 30  | 31  |
  |  I  | II  | III | IV  |  V  |
  | MAR | APR | MAY | JUN | JUL |
  |-----+-----+-----+-----+-----+
  | 31  | 30  | 31  | 30  | 31  |
  | VI  |VII  |VIII | IX  |  X  |
  | AUG | SEP | OCT | NOV | DEC |
  +-----+-----+-----+-----+-----+
  | 31  |28/29|
  | XI  |XII  |
  | Jan | FEB |
  +-----+-----+

> To a person who natively thinks in Roman numerals, remembering that the short months are: II, VII, XII, along with IV & IX would be much easier than the way us modern folks have to memorise it.

[1] https://www.benjoffe.com/fast-date