This is the way I think. C is "nice" because it is constructed to satisfy so many "nice" structural properties simultaneously; that's what makes it special. This gives rise to "nice" consequences that are physically convenient across a variety of applications.

I work in applied probability, so I'm forced to use many different tools depending on the application. My colleagues and I would consider ourselves lucky if what we're doing allows for an application of some properties of C, as the maths will tend to fall out so beautifully.