A great example to illustrate this vitally important piece of practical OR would be this classic 1980's movie scene from the 'Policy Academy':
Always knew that cutting all those redundant classes at St. Joseph's in the 80s to watch a projection of a linear "English" comedy in the relaxed atmosphere within the bounds of the adjacent Brigade Road theater in Bangalore, India served the dual purpose of preparing one for a OR career. Is OR great or what :-)
There are many practice instances where a customer has been 'blindly' following the constraint "because". Opening the eyes of your customer (especially the upper management) to this fact could be a huge value add on your part. Furthermore, when it comes to optimization models, such insight into the actual business problem sometimes enables us to bypass a strongly NP-Hard MIP and instead work with something relatively simpler, like an integer knapsack formulation.
Take this wonderful real-world example from the book "The Art of Innovation", where IDEO was redesigning a major medical instrument for heart patients during balloon angioplasty. See the Google books excerpt here. The key observation here was that everybody assumed that the instrument was "supposed" to be operable by one hand. Why? well presumably because the old instrument makers marketed it as such, and after many years it became a "design constraint". By noting that the other hand of the operator was pretty much idle while firing up this instrument, the designers were able to eliminate this unnecessary constraint. This led to a much saner and user-friendly design that also helped eliminate the scary 'ratcheting' sound that used to come out of the older instrument as it booted up, which used to scare the gowns off heart patients! The new product eventually ended up as a win-win for both patients and therapists.
In practice, there are constraints, and then there are constraints.