If someone can’t fly safely without paper checklist in a simple single engine piston that they regularly fly then are probably unsafe when it comes to “the big scheme of things”, however, for perfect flying you need a good paper checklist to follow
To deal with emergencies in complex aircrafts with redundant engines & interacting systems there are no other choices than checklists, QRH/AFM/POH, however in most single engine emergencies checklists, I come across do some logical: A & B and finish with “land ASAP”
I religiously use paper checklists when swapping types, even read whole POH/AFM and write a V-speed cards, other than that when I am current, I can just fly with memory but using paper checklists from time to time as does not hurt to keep memory sharp and in check, but I am very convinced it’s not the checklist that will save me from coming down out of the sky in SEP: it’s usually lack of fuel/engine probably combined with wrong controls inputs…
At the end of the day it’s matter of “procedural” vs “logical” types & states of minds, at any point of time you need one of the two working, ideally both in sync, not having any is really bad