I know you said to disregard modern physics, but modern physics, the necessity for it, and the incompleteness of it, is the whole answer to your question.
All "why" questions are questions about what's "under the hood" - what more fundamental principles give rise to the principles observed, like the hidden functional parts of an automobile give rise to its external characteristics. Since you're asking on Philosophy SE, you're presumably trying to skip straight to the most fundamental principles known - the rules of logic.
However, to ask a meaningful "why" question, the phenomenon which we are asking "why" about has to be something real.
The basic answer to "Why does the universe follow classical laws with a particular character?" is the unsatisfying "It's a tautology: by making various simplifying assumptions that are known to be false about the real universe, you defined a fictional universe that follows your fictional laws." Or the equally unsatisfying "It doesn't: the universe doesn't follow the laws of classical physics, unless you make some simplifying assumptions that are known to be false about the real universe."
Despite the excellent predictive power and computational utility of classical physics within its domains of relevance, classical physics unavoidably predicts things that are obviously false: atoms that can't form molecules and do chemistry, stars that can't shine, computers that don't work, circuits that won't close because of slightly oxidized terminals, lights that won't light up, and so on.
We can meaningfully ask why the universe approximates classical physics under certain circumstances.
The answer to that question is well understood: the laws of classical physics, and the domains over which they are reliable, and all their elegance and symmetry, can be mathematically derived from the more fundamental models which make more reliable predictions about the universe, given certain limiting assumptions. For example, the expression of gravity predicted by general relativity, after a transformation to an appropriate coordinate system, reduces to Newtonian gravity when distance to the center of mass of a system is large relative to the mass of the system.
This is not accidental. Since classical physics predicts reality very well under certain conditions, no more-fundamental theory which could not be mathematically re-arranged into a restatement of some aspect of classical physics under the same conditions could be true.
The universe is most accurately modeled by some combination of the Standard Model (an extension of quantum mechanics), General Relativity, and Statistical Mechanics - a branch of physics initially derived from classical mechanics that nonetheless makes good predictions in domains where classical mechanics doesn't work. It might be hypothetically possible to reconstruct StatMech from scratch starting from the Standard Model, reducing us to a combination of just two - I don't know.
These are what is "under the hood" of classical physics, its domains of relevance, and all their characteristics, including the ones of interest to you.
These theories (especially the Standard Model, which doesn't have gravity, and General Relativity, which is all about gravity) rely on incompatible axioms. Although they can be mashed together into useful effective theories, they are thus essentially incompatible. (Effective theories are like theories except that they do not purport to have anything to say about the real nature of the universe, only to make good predictions about certain types of real systems).
This suggests that our best theories are each slightly incorrect and slightly incomplete reflections of an unknown deeper set of physical laws. So the universe almost certainly doesn't follow GR, the Standard Model, and StatMech, either, unless you make some simplifying assumptions that are known to be false about much of the real universe - although very nearly all of the universe comes very, very close.
Those deeper laws, if we ever find them, will be the answer to why GR, the Standard Model, and StatMech have such elegance and reflect such symmetries in nature over their own domains of relevance. We find some hints about their character examining GR and the Standard Model (as Boba Fit describes in a previous answer), and some promising work-in-progress candidates (string theory, loop quantum gravity), but no answers yet.
The yet-unknown laws under the hood of modern physics may or may not turn out to represent a single unified theory - that is, their various parts don't rest on incompatible axioms, and its mathematical expressions reproduce the mathematical expressions that we know work under the circumstances in which they work. If they do, we'll be in a position to go looking for reasons of pure logic why the universe should have such character as to have those yet-unknown laws. For now, we don't know enough to begin to speculate.
We can take guesses at the answer. But in the end, the answers don't mean much without knowing the question. "Why does the universe have the laws it really, truly has, everywhere and always?" doesn't mean much without knowing what laws the universe really, truly has, everywhere and always. Like in Douglas Adams' Hitchhiker's Guide to the Galaxy: even if we somehow guessed the right answer, we would still need to know the meaning of the question to really understand it.