You would have to go back to James Clerk Maxwell's original 20 equations to see what it's all about. Okey, quaternions are kind of hard, I'll admit to that, but all in all it makes much more sense.
It's useful to be able to explain things to laypeople and the not mathematically inclined, which means tightening up the metaphors.
So you can't just do the math because we don't have all the math.
You won't really run into the atom stuff until you try to do something like calculate dielectric constants analytically, though self-energy is definitely a pretty easy trap to fall in even for macroscopic stuff.
I teach my children that we live in a sea of energy and that you can feel it when you move. It makes much more sense to them than trying explain inertia.
I tell them that of you rotate something, it will make an energy vortex making stuff seem heavier - and I show them with a gyroscope.
Then I explain that electrons are just like little gyroscopes, but of only energy. And it all makes sense to them. They don't think it's hard at all.
Not ... really. The problem is that we teach electromagnetics using a 19th century pedagogy that assumes the existence of the Ether.
This works well for some things and makes them nicely closed form and simple. Of course, it breaks down for other things (motors are one of the big ones) where you really want a field description.
Of course, a field description makes nothing simple and closed form. So, it isn't good for making exams out of.
If you can deal with 4-vectors, "Collective Electrodynamics" is a really good book.