Perhaps we need to look at terminology again. Airlines have checklists. One pilot does it and the other checks it. Unfortunately in single pilot operations and in most training we tend to use the 'checklist' as a promt list. Gee, what do I have to do next? Some pilots tend to rely on the promt list too much. "Why did you not turn the radio on?" "It's not on the checklist". The single pilot, or student, should have the list in his/her head and then use the printed list to check he/she has not forgotten anything. The list in the head can then be used to check that he/she has not jumped a few lines on the paper list. That way the paper list can disappear out of reach and the pilot is not lost. It always makes me wonder why commercial pilots are so dumb that they need a paper crutch and PPLs are so smart that they can do without.
I would have thought that a (CASA) flying school would have an Ops manual with checklists approved / accepted / checked by CASA and written procedures for the use of them. I also would not hire an aircraft from a school where the CFI frowns on their use. Did the last pilot do his/her shutdown check correctly?? I do not want to check for nicks in the propeller if it possibly is alive. Did the previous pilot fly the aircraft within its limits or am I going to be the dummy when something fails.