Let's say we describe a particle as being an excitation of a field. Can't we describe any physical phenomenon in the same way? For example, describe a football as an excitation of the football field. I think we all agree that this description does a terrible job of actually describing a football. In fact, I don't think it can be called a description at all. Likewise, I find describing a particle as an excitation of a field to be equally unsatisfactory.

I'm saying that a mathematical representation of a physical phenomenon isn't the physical phenomenon.