To return to the subject of crosswind limits.
Having just retired after forty six years of flying my understanding is simply this.
The demonstrated cross wind component is only that supplied by the manufacturer given the actual conditions used to achieve what they thought a useful limit might be. They could have spent more time and effort achieving a higher one but chose not to do so. It is what it says, a demonstrated wind that may not be limiting.
The aircraft operator and/or owner may then set a limit based on this figure that any operating pilot would have to adhere to.
The reason that the figure becomes binding is simply that if you have an accident or incident the insurance company can (and in my experience will) have perfect reason not to pay out, to either the operator or third parties. Saying to them that there was no set limit will not work. In the absence of an operators limit the insurers will use the flight manual demonstrated component to get out of paying.