Engineering is not the harbor of ignorance.
It really is. A working engineer might need to worry about annealing of copper in a dubious glass to copper seal one day, then coefficients of a biquad filter the next. So for that matter might a physicist. There is too much to do to maintain a clear working understanding of something that has never and probably never will come up in their career.
You see, in the past, engineers had insights in physics, that's why many of them contributed both to engineering and science.
Engineers number in the millions now. The type of insights you're talking about seem to come from once in a generation people, and from times when it was a lot more practical to make a notable fundamental contribution to science. Where are those opportunities these days?
Now engineers are seen as dogmatic people who cannot think outside of the box.
Engineering is mostly a commercial task-based function. Thinking outside the box can get you fired.
People you have to be careful not to trigger when you want to expose something that go against their preconceptions.
That's just belief at work. The dubiously existent backfire effect. Maxwellians have been equally triggered by comments which go against their worldview. It happens in medicine, and just about any situation where people are indoctrinated. It doesn't mean it's wrong to reject new facts, just that it is a process that has to be gone through when unacceptable contradictions arise.
More importantly, I don't think this "triggering" is as serious as you make out. Engineers are pointing out working realities that physicists might miss, and taking on the challenge of being "triggered" for a bit of fun and the opportunity to have a say. Neither Dave nor Mehdi actually disagreed with the core findings of Derek's video. I don't think any trained engineers on this forum have seriously taken exception to any core fact. I have trouble accepting an opinion that power 'flows' in a completely static magnetic field, but I am not arguing against the fact that Poynting's model works. Therefore people aren't arguing against fact or evidence. Nothing is being "exposed" beyond some raw nerves over things like education and the realities of an engineering life.
These engineers think they "own" circuit theory. They don't understand that circuit theory is just as physics as the Maxwell equations are. In fact circuit theory is just a special case of them.
No they obviously understand it and aren't arguing against reality. They are pointing out some impracticalities to going full-academic treatment. Yes, some people are rallying against the message (on YT comments etc), I don't think any are formally trained electrical engineers.
Some of these things lamentable, I'm not saying I like them or disagree with your sentiments, just pointing out facts.
No one has come up with a clean solution. Transmission line theorists, antenna masochists, electromagnetic solverists, or wire unreelists for that matter.
The solution was given by Derek. You have a Poynting vector pointing directly from the battery to the load. The electromagnetic field propagates at the speed of light, so energy will first arrive at the load at exactly 1 m/c seconds. That's simple and elegant. AND there's no other "approach" to the problem. Other "approaches" will give you the wrong answer.
Another approach is to say nothing propagates faster the speed of light, and through capacitance or magnetic induction, that's what happens, it can't be faster than 1m/c and the other answers aren't reasonable. That is simpler and eleganter.
Poynting is not needed, because the question is about current, not energy or power. Closing the switch is expected to cause a current burst, which creates a magnetic field, this travels outward and turns on the lamp at any current.
Maxwell is not needed, because a magnetic field will propagate without EM radiation to an infinitesimal degree over the distance, from an infinitesimally short dipole. One might guess to a correctness testably comparable to Maxwell's discovery, that the speed of light is involved.
I'm not rejecting the Maxwell-Heaviside-Poynting idea though. If I understand it, and it works, why would I want to do that? If I don't understand it, and have to take it on faith that it works, then why would I reject it? Despise it through jealousy at being unable to comprehend? Then how come all these engineers got their degrees?
Edit: Oops, I deleted the main point of this section: In the original video, Derek's speed of light answer comes from an argument made from a simplified description (like my reasoning now above). Comparing this to a clean solution (in the sense of what a field solver would arrive at) is like the time I told a teacher I had done my homework and it was "in my head". Simple and elegant isn't clean and correct - it's one of the mistakes academics make.