3. Maxwell's equations are difficult to view as a whole since they are 6 or 7 separate things that should each be understood individually. This is true of Newton's 3 laws too, but they are easy enough to bring together that you can teach them to high school students. While it is true that Newton's laws are about different things too, I find it personally more coherent to call them "Newton's Laws". Maxwell's equations are to me more like "Maxwell's List of Equations". Maxwell also served a similar role that Euclid did: He did a lot of curation of contemporary results.
Edit: In terms of point 2. I think as you say that Einstein was in fact not the first to make that assumption. Maxwell already knew about it, and his contemporaries did, but Einstein was successful in taking the assumption (about light being constant) further.
> Maxwell's equations are difficult to view as a whole since they are 6 or 7 separate things that should each be understood individually
How so? You can't understand electricity and magnetism separately because they both affect each other; the clearest triumph of Maxwell's equations is that they describe electromagnetic waves, but you need the complete system of equations to do that.
I guess this description is subjective in terms of wholes or parts, but to me the each of the equations in isolation makes sense too. They all handle separate parts of electricity and of magnetism. For me, personally, I find it difficult to visualise them all at the same time. I have to look at each one carefully and then relate that to the whole which would be what we now call electromagnetism.
If someone taught you that way they failed as a teacher. I am sorry to say that but they are a whole (with the exception of displacement current which needs Faraday tensor (which you can get relativistic invariants from too) to understand)
Maybe one can approach this from the other side. Knowing electromagnetism today, what is the most complete and simple framework for modelling it?
The set of equations from Maxwell's book are to me a heterogeneous presentation. If there is a category of electromagnetic objects or perhaps some other pure mathematics framework that synthesises everything together, then I would call that thing the whole.
Sure. You can start from relativity and show that for example the antisymmetric Faraday tensor (P in the link [1] below) can get you a lot of phenomena (not all the way, accelerating charges are hairy, even for Feynman, see the link [2])
To note, the reference to finding the relativistic invariant from the tensor in the first link goes back to the first edition of Landau and Lifshitz. The problem was removed from later editions because only a masochist wants to find invariants of 4x4 matrices by hand.
3. Maxwell's equations are difficult to view as a whole since they are 6 or 7 separate things that should each be understood individually. This is true of Newton's 3 laws too, but they are easy enough to bring together that you can teach them to high school students. While it is true that Newton's laws are about different things too, I find it personally more coherent to call them "Newton's Laws". Maxwell's equations are to me more like "Maxwell's List of Equations". Maxwell also served a similar role that Euclid did: He did a lot of curation of contemporary results.
Edit: In terms of point 2. I think as you say that Einstein was in fact not the first to make that assumption. Maxwell already knew about it, and his contemporaries did, but Einstein was successful in taking the assumption (about light being constant) further.