It's at best a leaky abstraction but for some domains it is very useful. Antennas are 'magic' from the point of view of Ohms law and so on but once you move to the electromagnetic domain you will find equivalents for most of the elements in the original abstraction: impedance, reactance and so on.
No, they are just non-linear: as the voltage goes up the current goes up in jumps because the resistance changes in a non-linear way, but it is still resistance and you can still express the system at any point of the curve using Ohm's laws and you can still compute the power lost in any part of that system using the simplest equations. A coil or a capacitor (or even a piece of wire, but there the effects are very small) are components that do not follow Ohm's laws, you need to add more parameters than just current, voltage and resistance to work out what's happening.
The electric field is very tightly constrained around the wire. The amount of energy that reaches the light through the gap is incredibly small, not nearly enough to turn on a real light bulb. The bulk of the energy does indeed have to take the path through the wire. I find that video usually leads people to an even less correct understanding than the marbles-in-a-tube analogy.
The Veritasum video can essentially be summarized, "fun fact: two parallel wires act like an antenna, and an extremely small amount of energy reaches the other end before the rest of the energy takes the long path through the wire.
I'm not sure circuit theory states that energy flows within wires? Current, yes, but energy transfer is the product of current and voltage, and voltage of course exists only between wires.
The Poynting vector is the obvious choice but we cannot do the experiment to tell between the various possibilities one can get by adding more terms that obey the constraints.
Energy does flow 'inside' a wire at low frequencies. The skin effect gets higher and higher as the frequency goes up until you reach a point where it is all skin effect. But even that 'skin' isn't idealized it definitely has a thickness, about 30 u at 5 MHz and 6.5 at 100 Mhz.
No. DC energy also flows around the wire. And I mean around, entirely outside of the conductor, not in the skin or anything like that. In particular it's not the electrons that carry the energy, though they can receive it from the fields and depose inside the conductor (like in a light bulb).
Wires, or conductors in general, are so useful because they allow us to manipulate the EM fields and channel the energy very efficiently.
It's an very common misconception coming from circuit models.
(the movement of electrons, and thus the deposition of the energy via "resistance", may indeed be limited to just the surface of the conductor; this is what that calculator shows)
Complete nonsense, the current carrying capacity of a wire is directly proportional to the surface area of the cross section of the wire. If it were the skin it would be proportional to the circumference and it clearly is not. I have no idea where you came into this idea but it is just completely wrong. You can test it for yourself with $50 worth of gear.
I'm not sure how do you plan to invalidate Maxwell's theory, which shows that energy flows entirely outside of wires, with $50. Or any other amount of equipment. It would be very much welcome in the physics community.
This misconception is even more widespread than "planes fly because of Bernoulli" because it's so incredibly useful when designing most circuits/PCBs. Though it is, fundamentally, a lie.
PS. Circuit theory is made to match reality for the case showed in the video via the concept of a transmission line.
@H8crilA is talking about energy, you are describing current. Energy flow is the product of the electric and magnetic fields [1]; electric field within a conductor is zero, therefore energy flow within a conductor is zero.
Yeah exactly. In particular a flow of current (movement of electrons or other charged particles, measured in Amperes) is not required for energy transfer, though it is a part of the efficient way of energy transfer via conductors/wires. Including in PCBs and even inside of integrated circuits.
The one is a special case of the other, it doesn't make the former wrong but the latter gives better answers in situations where the special case constraints aren't satisfied.