The idea that nothing is happening at DC so the energy cannot flow through the fields is a misconception. At DC, AC, whatever, the electrons are exchanging virtual particles. That's why energy flows in the fields, even if the fields are not changing or moving.
Yes, in QFT the fields are explained as exchanging virtual particles. But I think you missed the point of Farmer's video. As she pointed out, those exchanges are much, much more likely to occur along the wire rather than across the space. If you actually used QFT and math to map all that out, you would indeed get fields that would match up with classic EM and the results would not 'disprove' Poynting or anything else in non-QFT physics. But, if you actually DID all that--and I'm sure you aren't--the resultant fields, Poynting vectors and S-fields would not look like much the dramatized versions we have been seeing here with big arrows going through space from a battery to a load (and, b/t/w, omitting the equally big arrow
going the other way from the battery).
Now as far as Derek's video, you continually misstate what others have said in order to prove them 'wrong'. I didn't agree with Dave when he called you a troll, but I'm starting to wonder. If you were to open the ends up on the long pairs of wires, you know full well that no current would flow through the load in the fully settled DC steady state and no power would be exchanged over that space via virtual particles or Poynting vectors. You know that full well not because you will examine it with math, Poynting, QFT or advanced physics concepts, but rather because you simply apply Ohms law just like the rest of us blockheads.
Dave thinks that the Poynting vector does not work at DC because he is a circuit-headed engineer. The only way he can think of the energy traveling through space is when you have AC or RF. At DC no worky, because capacitors, transformers, and antennas, which are the only devices he knows that allow the transmission of energy through space, block DC.
IIRC, Dave and almost everyone else here has not somehow stated that Poynting's Theorem is incorrect. You keep bringing that up and it just isn't true. However...
The Poynting vector is weird, but it is what is really going on there. Welcome to reality.
...I think you may be misinterpreting the meaning of the Poynting vector as opposed to the integration of the S-field over a closed surface. Maybe. I really don't know. I'd have to think about that. I'm not a Poynter.
But, but, but, Derek did that in his video! Why should I redo what is already perfect?
Because his answer was the trivial 1m/c 'gimme' that we all understand, despite you attempting to repeatedly claim we don't whenever we omit the obvious.