You said that using the core is a "no teach", and that it's hard to not naturally use the core. I haven't found that to be true. Some put it together on their own, many - most, probably - do not. For those that don't, I usually start with the simple request of asking them to power the swing with the rotation of their body (get those hips turning!), rather than swinging with their arms. How they interpret and apply that instruction will dictate how things proceed from there. A lot has to do with the age and experience of the player.
This is exactly what I don't do!
Why do I want them to spin?
I do agree with most of what you say in regards to the differences via age and talent etc.
So you get a kid to find the core by teaching them to turn their hips. Do you know that a lot of instructors are teaching to not turn your hips? To resist that rotation? Ive been down the rotation and momentum trail. Its not what I consider the correct way anymore! I do not want to purposely turn the hips!