[TuringTest]

Certainly practical programming languages are not a one-to-one implementation of a theoretical model, but these models do create families of related languages that keep a close relationship and are separated from languages based on a different model.

Each time a new theoretical model is created to represent a particular programming problem, entirely new languages are created to ease the practical approaches of building systems for the underlying problem.

And it is worth keeping track of which models are good for which problems. So no, theoretical models are not good just for doing math with them, also for guiding practical usage.