The Simplest Hypothesis Possible

A big current can thus flow without the electrons inside the conductor moving rapidly. Though I should add they are in fact wave-particle entities and are formally indistinguishable from each other
What gobbly-gook!! and mis-information. And "don't tell anyone in STAT Id:(, Preposterous.
 
You are so confused. What you are describing is the generation of low voltage DC current via galvanic (or voltaic) and electrolytic cells, and they involve Redox reactions at the plates depositing or removing metal from the plates. As I mentioned earlier, which you failed to comprehend, the role of the ions is analogous to that of dopants within semiconductors (and yes, I read your if-ish overview on semiconductors): that is to provide electrons to support current flow. Don't get into the habit of projecting one piece of Physics practice (here chemical batteries) into another context.
There is no way an electrolyte provides a supply of electrons. It consists of an electrically neutral mixture of cations and anions. I can see no reason to think that processes involving voltage of 2000V or so, applied across a distance of the order of 10cm or so, i.e. an electric field strength of the order of 200V/cm, will cause electrolytes to release free electrons. I think you are just making this up. But if you have evidence for it, I'd be most interested to read it.
 
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So heat provides enough KE to overcome the work function, electrons actually fly off (hence vacuum tubes, CRTs, electron microscopes), and a supply line is actually ferrying in more electrons and maintaining electron density. So electrons can actually flow in such a circuit, and it's not just them jiggling (or having a small net flow or drift) while emf propagates through? I retain some cognitive dissonance over this. But your later post does clarify somewhat.
Just to come back on your point about heat, thermionic emission causes a kind of “vapour” cloud of electrons above the metal surface. So one can think of a sort of latent heat being absorbed to overcome the work function and get electrons out of the metal surface. I found it interesting in the articles on arc welding that they refer to a cooling effect on the cathode, resulting from this, whereas there is a corresponding heating effect on the far side of the arc as the stream of electrons is absorbed. This seems to be the reason for the 1/3 : 2/3 heat distribution between the two which is why it matters which way round the welder decides he wants the current to flow (if it’s DC).

Also in electrochemistry the fact that metals can be deposited, and gases released, at the electrodes is evidence that real electrons must be being supplied at the cathode and removed at the anode. If it were just “forces”, these tangible chemical changes would not be possible.
 
There is no way an electrolyte provides a supply of electrons. It consists of an electrically neutral mixture of cations and anions. I can see no reason to think that processes involving voltage of 2000V or so, applied across a distance of the order of 10cm or so, i.e. an electric field strength of the order of 200V/cm, will cause electrolytes to release free electrons. I think you are just making this up. But if you have evidence for it, I'd be most interested to read it.
Yes, electrolyte is an essential component because, as for dopants in semiconductors, it provides a source of electrons that support current flow. Without an electrolyte, wood acts as an electrical insulator and nothing happens: certainly no current flow. Anions carry a negative charge in the form of one or more surplus electrons in their conduction band, which are available to move under the influence of an applied emf, bumping each other along towards the positive electrode and allowing other electrons to enter from the negative electrode, and with an equal number of electrons being consumed by the positive electrode. Hence we have an electric current through an electrically neutral ionic solution. Why are you so blinkered?

With your ionic charge transportation system you have provided no mechanism for the anionic charge to be transferred to the positive electrode because there is none, nor any means for electrons to enter from the electrode: all done with smoke from where the sun doesn't shine and ionic mirrors I suspect.
 
Yes, electrolyte is an essential component because, as for dopants in semiconductors, it provides a source of electrons that support current flow. Without an electrolyte, wood acts as an electrical insulator and nothing happens: certainly no current flow. Anions carry a negative charge in the form of one or more surplus electrons in their conduction band, which are available to move under the influence of an applied emf, bumping each other along towards the positive electrode and allowing other electrons to enter from the negative electrode, and with an equal number of electrons being consumed by the positive electrode. Hence we have an electric current through an electrically neutral ionic solution. Why are you so blinkered?

With your ionic charge transportation system you have provided no mechanism for the anionic charge to be transferred to the positive electrode because there is none, nor any means for electrons to enter from the electrode: all done with smoke from where the sun doesn't shine and ionic mirrors I suspect.
I just have a chemistry degree. If you think that makes me "blinkered" you are entitled to your opinion but you need to show me why chemistry has got it all wrong for the last 200 years.

It seems fairly obvious there must be cations as well as anions in electrolytes. If there were not, there would not be metals plating out, or gases evolved, from the cathode when a current is passed through it. These materials that appear at the cathode are clearly the product of electrons neutralising +ve ions. So cations must move towards the cathode to be neutralised: positive charge carriers. Similarly, at the anode one has anions giving up electrons to the anode and generating gases like chlorine, oxygen and so on: negative charge carriers. And thus the circuit is completed, with electrons passing from the wiring into the electrolyte at the cathode, and passing from the electrolyte into the wiring at the anode.

If there were just free electrons passing through the electrolyte, these chemical changes would not occur.

It makes no sense to speak of a conduction band of anions in solution. A conduction band is a continuum of energy levels, formed by the merging of atomic orbitals in an extended solid array. In solution you do not have this. Anions and cations are individual charged atoms (or molecular species, such as sulphate), each surrounded by a solvation shell of solvent molecules that isolates it from the next: https://en.wikipedia.org/wiki/Solvation_shell. There is no continuum of states for their electrons to occupy - and thus no band.

You cannot read across the band theory of conduction in solids to solutions.
 
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