BPF
I think I mostly agree with you, several years ago I worked for a club who were a contractor for the MOD/RAF flying scholarship scheme. For their trainees, CFS insisted we talked through a similar T/O emergencies brief. They always handled simulated EFATO exercises noticeably better than the "civvie" students or PPLs. Now you might say that possibly it was due to a higher quality student, or that they were flying several times a day, most days for a couple of weeks. But maybe, running through the scenario pre-departure actually helps.
As to getting too checklist happy in the air, in my experience, if someone with relatively low hours, gets a simulated engine failure at a couple of hundred feet, it's pretty much all they can do to remember to lower the nose and maintain a safe speed, then try and land it somewhere. Both of which are vital, they rarely have the time/capacity to start distracting themselves looking for switches or telling the tower what's happening. It does of course depend how much height they've got before it happens.