Indeed, this example of a simple harmonic oscillator is not a practical use case, but more of a simple example and pedagogical tool.

There are potential use cases for more complex problems. Many complex physical systems are governed by partial differential equations, however it is often impossible to write explicit formulas for the solutions to these equations, and so the physical states must be experimentally observed as they evolve or else computationally demanding high-fidelity simulations must be run, sometimes on supercomputers for many days, in order to numerically estimate how the physical system evolves.

Just think about recent work in protein folding. Would a deep NN that tries to make protein folding predictions benefit from knowing physics-based constraints?