But I would argue that this parsimony is illusory. There's a lot of implicit knowledge needed for the interpretation of physical laws. The laws are written using specialized mathematical notation such as special functions, partial differential equations, in a certain conceptual framework such as Lagrangian mechanics. You need to understand the concept of abstracting and quantifying a dynamic system (most people wouldn't imagine you can do this) and then you have to learn all the tips and tricks of how to reformulate and solve systems.
For example, I could write a mathematical representation of quantum electrodynamics (the theory of how electrons and photons interact) on a single index card. However, I would need to dig into my two shelves of QFT textbooks to actually make any quantitative experimental predictions, on top of my degree, PhD and post doc experience, which I need to even be able to read the textbooks (and I would still mess up the minus signs).
I think it's important to remember that these neural networks are doing all of that - not just finding the physics, but also all the abstraction, calculation and interpretation that is usually taken for granted but actually very non-trivial.