Not a physicist, but I spent some time on this, exploring the possibility of a "teach scale down to nuclei, then nuclei up to matter" learning progression for primary school.
Nuclei are quasi-classical little balls. It's electrons that are wacky quantum weirdness.
Which makes the current pedagogical emphasis on electrons, rather nuclei, as a foundation for understanding atoms... perhaps miss some opportunities for greater clarity. And that's even before getting to state standards that require teaching both "atoms are conserved in chemical reactions" and "atoms are electrically neutral, so if charged, they are no longer atoms, but ions". Sigh.
Nucleons overlap (not orbit), but nuclei aren't homogeneous, especially light ones. Light nuclei are well described as clusters of alpha particles, heavier ones as liquid drops. Ground states are generally more or less spherical. Though Neon looks like an old-style wine bottle, with a tetrahedron of alphas in the bowl, and a fifth making a neck. Non-ground states for lights are mostly rearranged alphas, for heavies, variously distorted balls. Fission is droplets stretching and necking apart.
A proton is a mix of odd shapes, but directly measurable properties are spherical. It's just a ball.
Nuclear mass and charge density are, to a good first approximation, colocated. You don't have mass concentrated one place and charge somewhere else. No surprises.
Electrons are a peak with exponential falloff, making choosing a radius quite arbitrary. What's the diameter of a cartoon volcano, that blends seamlessly into plains? Wacky, wacky electrons.
Nuclei have a flat-ish density plateau, then a steep slope, and only then a tiny exponential footlands (Woods–Saxon potential). So it's just a ball with a fuzzy edge, rather than a wacky exponential cloud thing.
Note the narrow range of sizes being discussed. No one is suggesting 10 femtometers, or 0.1 femtometers, or even 1.0 fm or 0.8 fm. "GEOID-Next committee tables discussion and heads to a bar, unable to agree on the shape of the Earth!!! News at 11!!!" But for most everyone, primary school up, that's "a femtometer ball".
A superball can be bounced, and crushed, and burned. You need polymer physics to understand just why it behaves as it does. But you can describe that behavior to a Kindergartener. They don't need polymer physics. Nuclei are just little balls.
Now look at the giant hairy mess of this thread. It's like, we teach "4/3 pi r^3, 4 pi r^2", but not "the volume and area of a ball are half of its box". But dialed way way up. Science education, variously distracted, failing to provide a coherent briefing on the physical world.
If anyone has ideas on how to describe this point, I'd appreciate them, as I've never come up with something nice.
Here's a tiny Neon pic. I just think Neon is cute. https://arxiv.org/abs/1406.2473 page 4. There's a nicer one somewhere...