Is this an arcane rule? "Don't label divs" and "aria-label is for when there's no content in the DOM that can be read" are pretty simple rules. Labels are ways to tell a screen reader about content it can't read, like an image or icon. Pretty straightforward.

It's way way simpler than, say, var hoisting in JavaScript.

it's a somewhat stupid rule. People process information differently visually than they do via aural methods. If you have a reason why something should not be read by a screen reader, because say the order you would be reading it makes sense visually but not at all aurally, then you have to jump through hoops to visually hide the aural content, and then aria-hide the visual content, and there may be more complicated things dependent on button position etc.

Not be able to aria-label anything and have the screen reader say ok I take that in priority seems badly thought out.

Also - screenreaders could have a setting to read aria-label on divs and then read the content if the user wanted it. If the user determined the labels on divs were inadequate, they would flip this setting, if they decided this seems to be working well they would just go with what the site does.