For reference I use the revue technique moto for the Honda CB400F and Norton Commando.
They do say to use the idling engine method.
What I have read elsewhere is that if your horseshoe is binding or the spring is old the conventional method doesn’t work, as there is too much resistance for the spring and stem bit to set the slack correctly.
The fix is to use the « engine off , screwdriver inside » that you described.
I don’t have the shop manual right now, maybe there is something on there?
Anyway here was the information I have. I need to adjust the chain soon so I’ll keep an eye out