I think that comparing a briefing appropriate to Courchevel airport operations to that appropriate for any initial pilot training differ so much that they are hardly worthy of discussion in the same theme. It defeats discussion to confuse two such things into each other, when they just don't fit. A student pilot spends a lot of their time being task saturated - over saturating them is pointless. As the candidate gains proficiency (and perhaps becomes "crew") there will be an expectation that they can absorb and effectively apply the contents of an appropriate emergencies briefing. Before that point, the "supervising" pilot has an added burden to execute the intent of the brief, probably expecting the candidate pilot to do little or nothing.
Of course, we want the candidate to get used to an emergencies brief as a part of their proper habits in developing pilot skills. So, we always include it as a mental placeholder. It is imposed more to the candidate as they progress to actually absorb, and expect to execute it if conditions demand.
As for "closing the throttle". I train that two phases will occur in prompt succession after an engine abnormality: (A) Assess if the airplane can still climb away [at all] with the power available. If it can, continue with high preparation for significant power loss. Gently turn away from built up areas toward suitable forced landing sites. If you can make it around to a safe runway landing (not a "turn back") then continue, with preparation for a significant power loss all the way along. If, on the other hand, (B) the power loss is such that continued powered flight is not possible: Lower the nose to maintain safe flying speed, and gently turn toward the most suitable forced landing site mostly ahead of you. If you just did something which you think caused it, reverse whatever that was. If reversing gets you some power back, revert to (A). If it does not, close the throttle, and execute a forced landing as best you can. As is the case with about any planned execution of emergency piloting, I seek to avoid "changing your mind" from one emergency action, to another - make the plan you judge to be best, and follow it through to complete as best you are able.
Of course, the foregoing stream of consciousness is hardly an emergency brief, it's way too long and wandering. It is "training" conducted in the class room. The emergency brief in the cockpit just before the throttle(s) is open is much more succinct, and hopefully tailored to the airplane type, local, crew capability, and conditions. That is why it is not a one size fits all.
Any emergencies brief is a mental placeholder that something could suddenly happen at low altitude, which will wholly change what your flight is going to be, and a plan for that would be a good idea. It should be appropriate. It should not contain elements which are not applicable.
Do I recall that operations in and out of Courchevel requires a pilot "qualification"? When we start talking about airports which require special qualifications to operate, emergency briefings probably take on a form beyond the general theme of this thread! But hey, if some is familiar with a typical emergency briefing appropriate to this airport, feel free to post!