"Your claim that there is such a thing as "the relaxation that was needed when first arriving onto step 1" is just silliness. Even if there were some part of the dancer's form that would be relaxed at such a time, it would not be the core."
If you wish to fully utilize the energy available in the downswing, you need to release the muscle tension you are carrying into it. Since there are not at this point any forces due to movement that would distort your body trunk, you really do not need any more core tone than you would have if you were just standing around in a non-dancing mode.
". . . the times when we are simply following our inertia with our body vertical, . . .
There are no such times."
You will be a much better dancer when you discover them. Dancing is not about work, work, work - it is about the cyclic transition between drive and drift, and between fall and rise.
"Also, I have no idea what you mean by "excess tension." Do you seriously believe that some dancers could be tightening their core too much?"
Absolutely, it is an extremely common problem.
"Are there any recorded instances of a dancer suffering a hernia, for example, due to extreme exertion of the abs and glutes?"
I'd be surprised if there weren't. But that's largely irrelevant. Over use does not have to risk injury in order to be detrimental - the minute it starts limiting the needed release it becomes a problem. Luca Baricchi has or at least had a great lecture on this on youtube - though in my opinion he argues for taking the relaxation too far.
The essentially skill is to be able to have one muscle activated to sustain an aspect of posture that could not be maintained against otherwise, while having another immediately next to it, or its sibling on the other side of the body, entirely relaxed to permit a range of movement that could not be achieved otherwise.