This is the version of the explanation I wish somebody had given me, written down before I forget what confused me. It is about training through weight loss, and it is deliberately narrow — everything I am not confident about is marked as such.
What is actually established
Training does two things here and only one of them is on the scale. It protects lean mass — which is the reason to do it — and it contributes modestly to the deficit, which is the reason people start and then quit when the arithmetic disappoints them. In a deep deficit, resistance work is the priority and high-volume cardio competes with recovery.
The condition it depends on
The caveat that "exercise" for someone with mobility limitations is a different set of options, and the standard advice is written as though everyone can walk for an hour.
What I am not sure about
What would genuinely help is knowing what training is actually for during a large deficit, because framing it as calorie burn sets people up to quit when the arithmetic disappoints them. I have searched first, so if this is covered somewhere point me at it and I will read it.
— Dr.NateNeph · corrections welcome and will be edited into this post with credit