Let’s pretend for a moment that I am working on designing an airplane and I need to hire an engineer to work on the project to do CFD simulations. Now, the Navier-Stokes equations are much too complicated to solve directly on the scale of an airplane, even on the most modern supercomputers, so CFD programs generally make a series of approximations that use “simpler” models to simulate certain aspects of the flow to get a good engineering answer. Now, if the guy running the CFD for this project never learned how to derive the Navier-Stokes equations, how am I supposed to have any sort of confidence in his ability to know what each of the aforementioned turbulence modeling methods means, what sort of approximations it makes to the N-S equations, and what the implications are to the solution the code spits out? In other words, how am I supposed to trust that this engineer has any clue that his CFD solution is valid?
I could make the same argument about designing the internal components of an engine at Ford or John Deere, the external shape of the next Corvette, the external aerodynamics of a suspension bridge (hello, Tacoma Narrows Bridge), and so on. If a new hire never learned the fundamentals, I have no reason to believe that he or she has the ability I need to understand the implications of various settings and models built into any commercial CFD package, and I have no reason to believe he or she will have any idea how valid the output of the code is.
Another quick example would be the ability to draw conclusions based on incomplete information. If someone has a good grasps of the fundamentals, such as the meaning of various terms in the N-S equations, they can usually use incompletely information to draw conclusions much more effectively based on reasoning through the features of the governing principles of a problem. This applies to the above example when an engineer has to assess the validity of CFD results, but it also applies to many other situations. Any time an engineer is reading through a set of results of any kind of engineering analysis, interpreting those results is going to be easier if he or she has a grasp of the relevant fundamentals.
Is that a job task that every single mechanical (or aerospace or civil or chemical) engineer is going to have to perform in their career? No. But enough will have to deal with it that it makes sense to learn it. You could make the argument that these people could just learn it on their own as needed and not burden everyone else with such topics, but then you could use that same logic for essentially every core course in an engineering curriculum. Where do you draw the line? Should engineers not take physics because they are almost never going to have to know about a cart rolling down a hill? Should they never take calculus because they will not often be required to perform a derivative in their job? Where do you draw the line?