Huggy... my turn to say "spot on", mate!
Checkie... how regularly did your students fly? Were they all looking for a career in professional aviation? Or, perhaps at least some of them were only going as far as a PPL? I don't ask that last question to demean PPLs in any way ... the simple fact is that most of them don't fly quite as often as the rest of us.
Practice is what makes perfect. Without the continuity, what chance does any pilot have of keeping any checklist in memory? Having been an instructor myself, I know the answer to that question as well as you do.
How many times have you heard of an aeroplane landing on its belly? The checklist, itself, won't prevent such an occurrence, but it can sure as hell be argued that the "memory system" failed the acid test. It's all discipline, of course, but even THAT has to start somewhere.
I've always believed in starting with the imposed discipline of a checklist. It lays the ground rules for good airmanship, no matter how you interpret that word.
The best checklist system I've found, to cover all those airborne checks, is the type that mounts on the glareshield -- plastic tags that you flip down in the pre-take-off and climbout checks, or flip up in the approach and pre-landing checks.
They facilitate looking outside the plane as you're going along. They hold the place that you get up to in the checks, which is just great if you get distracted for any reason. And they're easy to use. They're not on all aircraft but I've flown quite a few aircraft, even in commercial operations, that were fitted with them. Made life very much easier, especially on high workload, short sector flights.
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Once a king, always a king.
But once a nite's barely adequate!