That said, I agree that there are a few aircraft flying out there which predate this requirement (pre 1949). I suppose with those, you just do your best if the POH provides no checklist.
Yes, some simple types (maybe homebuilds such as Nipper, Jodels etc) may be single seat and have no approved checklists. In those cases
maybe there is no mandatory requirement for (or availability of) an approved checklist.
But types such as the Chipmunk and YAK - no excuse there I think!
Just because you may have flown a particular type over many years and have gained a substantial amount of experience doesn't exempt you from the basic principles of good airmanship (TEM) - no matter how much faith you have in your own intelligence.
Remember the greatest cause of accidents is still 'pilot error'.
The use of checklists can only serve to lessen the likelihood of errors arising due to inadvertence on the part of the pilot.