The fact that there may be other elements besides the sign that influence whether or not parking is truly allowed is not the point. The point is that the sign "No parking between 7pm and 7am" is implicitly telling you that parking IS allowed between 7am and 7pm.
Is the sign giving you details about what type of parking is allowed? No, it is not. Could other signs offer more or even contradictory information about parking? Yes, certainly. Could the sign be completely and totally wrong in both the explicit and implicit information it conveys? Absolutely!
The phrase "the exception proves the rule" is not referring to mathematical proof that a rule exists and is valid. It is referring to the fact that we can deduce that the writer of the sign had an underlying rule in mind because of how they wrote the sign. We may, of course, be wrong...our understanding of the sign may be faulty, the sign writer may not have intended it as an exception. However, IF the writer did intend it as an exception, then our deduction must be correct--the writer MUST have had an underlying rule in mind.
Human communication contains gaps and unspoken assumptions--especially when it comes to norms. We don't tend to explicitly state what "everybody knows." However, this unstated information makes it very hard to have a rigorous discussion of human knowledge and behavior.
Thus, we are often left in the position where we need to explicitly state what "everybody knows." This can be quite difficult, since, sometimes, we are looking across time and outside of our cultural context--we aren't privvy to what a given speaker assumed his or her listeners shared as common knowledge. How can we find and delineate this information? Well, one useful way to identify unspoken norms is to look at stated exceptions to these norms.
Is this a useful thing to do? Well, that is like asking "Is division useful?" It depends on what question you are trying to answer and the type of analysis you are undertaking. It isn't hard to imagine someone misusing division to come up with an answer that is wrong or at least not useful. However, we know that division can also yield a useful answer. Similarly, there are problem domains where an analysis of unspoken norms, conducted carefully and properly, can yield useful results. It can also yield garbage if misapplied.