There are numerous blogs arguing for consistency in a UX design mostly for soft reasons, such as "it's good for company branding," "it’s just good design," and “it’s easier to learn.” Here is the most important reason for UX design consistency, based on how the brain works: Lack of consistency in a UX design leads to added “cognitive load” for the user and breaks the “transparent to task” effect.
Cognitive load: used in cognitive psychology to illustrate the load related to the executive control of working memory (From Wikipedia)
The brain can only handle so much load (short term memory and thinking processes) and then beyond that becomes overloaded and thus distracted or slowed down. In the field of UX, cognitive load is more casually used to mean the thinking load a user must do in order to accomplish a task. This includes the combination of thinking load required to use the interface and the thinking load required to accomplish the task itself. Ideally we want the cognitive load required to use the interface to be tiny so that the user’s mental processing capacity can be mostly devoted to the task itself.
For instance, on your phone there is a UX pattern for how an item is deleted. A dialog will appear in a particular way with standard buttons such as "Delete [item]" and "Cancel." The first time you see the pattern you spend the time to look at it and read the buttons. You pay attention to what you are selecting in order to get the result that you want. In other words, you learn the pattern — "So this is how I delete items." Once you are familiar with the pattern, you don't really need to think about the dialog or read the text; you see it and instantly recognize that it’s the delete pattern you know. You trust it and know what to do. Tap, and you're done.
If you attempt to delete an item and the pattern appears different, even by a small amount, you have to stop and examine the new pattern, i.e. read the buttons and think, “Am I doing this correctly?” The brain is good at recognizing that something is different from a known item, even if it can’t tell specifically what’s different. A different pattern, even if just in appearance, forces the user to re-evaluate how the pattern works. This kind of cognitive distraction in a UX — trying to sort out the meanings and similarities of a UX that is not consistent — is waste of cognitive energy.
On a UX with good consistency, the user will spend a reasonable amount of time learning the interface and once they learn it, the use of the interface controls can become automatic or, at the least, require only a small amount of active thinking. In the study of the human use of tools, this effect is understood as a tool becoming “transparent to the task.”
Transparent to the task: in the human use of tools, when the use of a tool is so automatic that the user only needs to pay attention to the task.
This is very well illustrated by driving a car. When you become comfortable driving a vehicle, you just drive it, and you don’t think, “turn the wheel to the left” or “push the brake pedal.” The controls can be used with very little cognitive effort and the car becomes transparent to the task of traveling. The more effortless a vehicle is to drive and the less issues it has (not making weird noises or about to break down) the more easily it becomes transparent to the task of traveling. In other words, the more perfect the design and implementation, the more powerful the transparency to task effect.
The same effect can happen in an application on a computer. A UX should be well enough designed and implemented that the user forgets about the UX design and just efficiently gets tasks accomplished.
An inconsistent UX requires the user to repeatedly allocate thinking to how to use the interface because there are many more variations of UX patterns. Consistency (visual and behavioral) in a UX means that the user can learn the controls and then employ them without much active thinking about them, and can instead concentrate on the work itself.