The idea that someone with equal ability to do calculations with both could understand Newtonian mechanics better than they understand quantum mechanics belies an extremely naive view of how easy it is to perceive the true metaphysics of classical mechanics. In fact, the metaphysics of classical mechanics remains unsettled even today, the only reason it seems like there isn't a lot of philosophical debates left to have is that it has fallen out of fashion. A brief conversation with any philosopher will reveal that nobody "understands" the basic essence of being or whatever you want to call it. In fact, if "understand" means "have direct sensation of the true nature of reality," or even "have some grasp of the true metaphysics," then nobody understands anything.

To give a specific example, let's say you have a classical system with only three particles in the entire universe, and further let's say they are interacting via a conservative force. So, how many things are there in the universe? Is each particle communicating with the others to organize their movements? Then, there would be three things in the universe. Is there a potential field permeating all of space, into which the particles project their influence? That would be four things. Is there a "strand of force" connecting each particle to every other particle? Then, there would be six things.

The debates in the paragraph above were alive and well in Newton's time. However they were philosophical debates, not physical debates, because the three suggestions I proposed (along with the other possibilities I didn't mention) are all mathematically equivalent and would lead to the same motion.