Why will I be bothered by that ?
And it doesn't bother you at all that there is no circuit you can put in region A in the diagram below that can extract energy from the wires that surround it? Even a DC/DC convertor? Even if you can connect it to a GND? But extracting energy from regions B or C is a piece of cake?
And I guess that it doesn't bother you if an isolated charge is placed in region A and it stays where it is put, but if the same charge is placed in B or C it will accelerate, acquiring energy ultimately suppled from the battery, without being connected to it?
And it doesn't both you if you charge a capacitor between +110V and +100V is has exactly the same stored energy as one charged between 0V and -10V? Even though one has been charged at a higher energy? And the other has been charged at a completely different polarity?
And it doesn't bother you that a transformer can get 95%+ transfer of energy from one wire to the other, even though the wires don't touch, and no charges from the input wire get transferred to the output wire?
And it doesn't bother you that for your version of electrostatics (sum of force between charges), every charge needs to be in consistent communication with every other charge in the universe, to work out how far away they are, and at what direction?
And it doesn't bother you that a transmission line is a series of inductors and capacitors, however on inspection those capacitors and inductors can neither be identified or isolated?
And it doesn't bother you that commercial radio transmitters can get kilowatts of energy to disappear into literally thin air?
You must be a firm believer in the Lumped Element Model. It seems to work, so to you it must reflect the mechanics of reality, rather than an useful abstraction and approximation that allows you to get stuff done.
Not sure where to start from but you have a lot of misconception about how things work.
Yes regions B and C have an electric field but you can still do not extract energy from that. Same with magnetic field that is also constant basically like a permanent magnet. Let me know how you extract energy from a permanent magnet and we can clarify from where you actually extracted the energy because it was sure not from the magnet.
Yes if you place a charged particle in an electric field it will be accelerated but note the action you take to put a charged particle there.
The potential difference for the capacitor is 10V in both cases and as far as energy is concerned it makes absolutely no difference. The zero/ground is something arbitrary that we chose.
If a capacitor is placed on the positive of two power supplies that have common negative tied together and we consider that the zero point then we connect a capacitor with one plate to positive of the 100V supply and the other plate to the positive of the 110V supply you just have a 10V potential and as far as capacitor is concerned that is all he will see thus it will store the exact same amount of energy as the one connected to what you call a 0 to -10V supply that can also be seen as a 0V to +10V supply is all a matter of definition or how it is connected to other things where you may already have defined a "ground"/zero point/reference point.
A single inductor is an energy storage device same as the capacitor is an energy storage device and so with transformer you can store energy by creating a magnetic field while supplying the primary and then retrieve that stored energy with the secondary or the other way around or with the same.
So by running a current through any of the two coils you are creating a magnetic field that remains there as long as there is no change in current flow.
If you suddenly stop the current flow by disconnecting the source voltage on the both coils (primary and secondary) will increase and so you can take that stored energy out through any of them.
But if you run a DC current through primary then you can not take energy out from secondary. You still have a strong magnetic field but it is constant so energy storage is maintained full.
Of course a transmission line is a series of inductors, capacitors and resistors and of course you can see them if you can see the wires of the transmission line and understand what a capacitor, inductor and resistor are.
The energy of a radio transmitter will not disappear. As a simplification is a capacitor with one plate as the transmitter the ground as one of the conductors and the other plate is the receiver again with ground as the common conductor.
The capacitor is charged and discharged multiple times per second depending on radio frequency and of course there will e a lot of power loss due to resistance in this circuit.
The lumped model works because it is a representation of reality. And yes it will be an approximation as in simulation you may use just like me hundreds of this groups for a 20m transmission line to keep the calculations manageable and the results more than close enough for what we need them.
If you think you have a better model that allows to make accurate predictions about what happens on a transmission line then please share as I will be curious to hear. I will like to see the equations not just some story.