> In particular a flow of current (movement of electrons or other charged particles, measured in Amperes) is not required for energy transfer

Of course it isn't, as any transformer or transmitter/radio would show you. But that's not what this is about. It's about as useful as telling architects to use quantum mechanics because that's the fundamentals of what they are doing or having every electronics design model each and every conductor as a transmission line. That's what Spice is for, to ensure that from an EM point of view the design is valid (and to ensure that you're not radiating EM).

But it's in the end a discussion about fundamentals and as you pointed out circuit theory is so damn useful that it gets you 'close enough for government work'. That there is a whole pile of field theory that you could use to model the same circuit is true but it isn't so damn useful and in practice would just complicate matters considerably requiring every electronics engineer to engage is high level math. Just like we're not going to ask carpenters and bricklayers (and architects) to take into account the fact that Newton 'got it wrong' and we should all be using Einstein's equations instead. But when you are designing satellites you should.

Engineering uses the tools appropriate for the task. If that tool is Maxwell's equations because we're dealing with stuff that should be modeled as a transmission line and the field component is the dominant one then so be it. But for most practical electronics circuitry you can use V/A/R just fine. When modeling capacitors and coils Maxwell's equations are applicable but you can likely still get away with approximations as long as you realize that that is what you are doing. When modeling a complex high frequency circuit things change rapidly and modeling your interconnects as transmission lines makes good sense because that is ultimately what they are and ignoring that aspect will make it much harder to design something that actually works.

So the statement that 'energy does not flow through a wire' makes sense in an EM theory view of electricity, which is fine for pedantry but won't get you places if you are moving bulk charge from point 'A' to point 'B' to get some useful work done. Just like EM theory in turn isn't correct either, the quantum physicist would tell you that your theory is 'just an approximation' and that you are 'doing it wrong'.

For the subject matter, antenna design the field is obviously the important part otherwise you're not getting anywhere at all. For DC to low KHz circuits that do not contain large inductors you will be able to keep things fairly simple. As soon as you start working with inductors you will have to 'level up' in your view of how the circuit works and if you don't you'll probably end up with something that is either sub-optimal or that subtly differs in its actual operation from what you think you've designed.

If you want to build GHz circuitry there is no way that you're going to avoid getting to know mr. Maxwell better, fact by then you'll be pretty intimately familiar with the underlying electromagnetic theory, it's unavoidable.

But for bulk energy transfer at very low frequencies it definitely isn't the skin that carries the energy, if it were you could replace all of your copper with foil and call it a day.