No. It is not always appropriate to minimize cognitive load.
Minimizing cognitive load is not the goal of usability, human factors, UX, or the user centered design process in general. It is about "good design", and good design is not always the simple design.
To clarify the rationale, let's make sure we have a definition for "cognitive load".
In cognitive psychology, cognitive load refers to the total amount of mental effort being used in the working memory.
To put it another way: how hard is it to figure something out, or how hard is it to accomplish a task. So when is it appropriate to actually make something more difficult?
Requirements of a system are not always strictly "make it simple to use." Many external forces and environment constraints often guide "good design" in a direction where it makes sense to make something more difficult, helping to prevent unintentional usage of either the intended or an unintended user.
Here is an example for The Design of Everyday Things, Donald Norman's classic book, in which a door is made more difficult to use:
Quoted from the book:
This is good design, deliberately and carefully done. The door is to a school for handicapped children, and the school didn't want the children to be able to get out to the street without an adult.
Continuing reading from The Design of Everyday Things:
Most things are intended to be easy to use, but aren't. But some things are deliberately difficult to use - and ought to be.
Designing something to be difficult can protect the user. Reducing the cognitive load may produce a situation where an unintended audience (e.g., children) can too easily use the system. It can also protect the intended audience from making errors.
Guarded buttons are a simple example of making a task more difficult for the intended audience. If you take a peek inside any airplane cockpit, you'll see plenty.
By making the task more difficult, the designer has reduced the chance of an operator accidentally pressing an unintended button.
User Experience is not about "easy".
ISO 9241-2101 defines user experience as "a person's perceptions and responses that result from the use or anticipated use of a product, system or service". According to the ISO definition, user experience includes all the users' emotions, beliefs, preferences, perceptions, physical and psychological responses, behaviors and accomplishments that occur before, during and after use. The ISO also list three factors that influence user experience: system, user and the context of use.
Notice that "easy" isn't in there. "Easy" is good, "easy" is an element, but it is the overall experience (the "anticipated result") that is the overall goal. Safety is a huge part of that.
The US Military has a Military Standard that focuses on Human Engineering (of which User Experience is related). MIL-STD-1472F, "Department of Defense Design Criteria Standard", discusses at length how systems should be designed to promote effective work flows and safety of the user. An excerpt of the Objective of MIL-STD-1472F reads:
Military systems, equipment and facilities shall provide work environments which foster effective procedures, work patterns, and personnel safety and health, and which minimize factors which degrade human performance or increase error.
The standard also has the following requirement:
4.8 Safety. Design shall reflect applicable system and personnel safety factors, including minimizing potential human error in the operation and maintenance of the system, particularly under the conditions of alert, battle stress, or other emergency or non-routine conditions. Design of non- military-unique workplaces and equipment shall conform to OSHA standards unless military applications require more stringent limits (e.g., maximum steady-state noise in personnel-occupied areas).
In many situations, making something "easy" reduces the chance for the operator to make an error. But sometimes the action needs to be made hard in order to achieve the user experience you are looking for - protecting the operator by making it more difficult for them to commit an error.