"The Poynting Vector is pointless."
Please, kindly, toss all your coax cables out the window then.
Apparently you missed the context. I was referring to steady-state DC circuits exclusively, which ironically I often use coax cables for--but that's a different issue. And I didn't say that they (Poynting vectors) can't be calculated, drawn or that they somehow don't apply--I said that they are poyntless in that they serve no purpose other than to give you the smug satisfaction that you are above all the other heathens because you somehow "know what is really going on".
Anyone who brings up poynting vectors in DC circuit theory will be laughed out of any engineering classroom or lab.
You say that but I teach DC and AC circuit theory at my university alma mater, so...
I wonder how many EEs, as opposed to physicists, have had a practical use for directly using Poynting vectors or Maxwell's equations since leaving university? Sure we all know the right- and left-hand rules, and an RF engineer might well have use them indirectly when using an EM or antenna modelling package, put I doubt most EEs will have touched them, or have had a need to do so directly, since leaving the classroom.
That's not the idea though even if you're right and it is a minority who ever do an actual Poynting Vector cross product. However, if I ask an engineer, 'where is the energy in the coax cable?' and they respond 'in the wire' then I know they don't actually understand how it works (why do different dielectrics create different characteristic impedances?). I mean, I am in awe of Heaviside's insight into the Poynting Vector and his DIRECT application of Maxwell's Equations to inventing the coaxial cable:
https://www.microwaves101.com/encyclopedias/multi-dielectric-coax"But my model is good enough for what I want to do! Who cares?" (things I've heard my students say)
Maybe, but as an engineering educator, I have NO idea what my students will be doing when they leave school. Maybe all they'll do is load calculations for residential construction - or maybe they'll become a top-notch RF engineer. I don't know. My job as an educator (and as a working professional mentoring interns) is to do my best to ensure they have the correct physics understanding of the underlying phenomena so they can apply it to ANY EM problem and arrive at the correct answer. They can make their own shortcuts and tools with this knowledge.
I'm doing a disservice to the profession of engineering if I handwave away Maxwell and say "well you'll never actually need this so I'm not going to show you where the shortcut comes from but just give you the shortcut..." and substitute the rote intuition of limited models applied to specific conditions for the actual physical theory whose simplifications have created the models.
Another good example of this is voltage transformation in a transformer. Yes - the turns ratio for voltage transformation is described by a simple fraction, but getting that fraction from Faraday's Law is quite interesting and provides tremendous insight into how AC asynchronous induction motors work (I make it a requirement in the class I teach). Will anyone actually be doing vector calculus over and over again? No, of course not - but they'll be well-suited to be expert engineers in knowing when the model works and when it doesn't.
There are reasons this theoretical knowledge gets tested to become a professional licensed engineer.