I think what is mandated is that there IS a checklist on board the aircraft.
What I think would be interesting to know is when you take a check ride, and you don't use a checklist, do you pass your check ride?
BTW: I am of the opinion that many items should be done via a "DO LIST" instead of a checklist. I AM NOT A FAN OF "FLOWS" to accomplish things. I have seen both methods and the most sure way of setting all switches prior to start is the "DO LIST".
"CHECK LISTS" make more sense while actually flying, moving etc.
IT seems to me that C150 types have a checklist printed on the sun visor. Piper had checklists printed on the instrument panel near the fuel gauges. But this is from memory as I have not flown either types this century. Or in the last 32 years.