I think a lot of over-analysis is happening here.
Firstly, is there really such a thing as
good situational awareness? It would imply that there can be bad situational awareness as well, which is a bit of an oxymoron.
The clue is in the name. Situational awareness is an awareness of a situation.
There are many tools that you can use to help you gain and retain situational awareness. Not all of those tools are applicable all of the time, some are even subconscious. Selective use of these tools, as appropriate (and with a personal preference) is the key to maintaining situational awareness.
Every aspect of instructing, every single bit of it, is about situational awareness.
Doesn't leave much room for actually teaching someone how to, for instance, control an aeroplane.