Your attempt to link this practice to different orders inside the Latin Church is not correct. Orders are not rites.
No they are not rites but that was the only analogy I could think of. Rites are governed by rules made by churchmen. Orders are governed by rules made by churchmen. Rites are written by humans in an attempt to find words of communal worship pleasing to God. I shouldn't try to compare apples and oranges.
Maybe it isn't that way in the Eastern church, but rites in the Western church have undergone many changes.