Memory checks flow around the cockpit, covering everything in order. When you are reading checks out, you often lose your place in the list, or read a check but not actually do it.
There are countless times where students, reading from a checklist, are happy to line up for a navigation flight without having set the DI properly, or reading "t's and p's in the green" without actually visually checking this.
Would you not agree that if the flow was clearly learned and defined and this was then backed up by a very short checklist that there would be less chance of a critical item missed on the flow being missed a second time when the checklist is completed.
People loose their place on the list becasue it is a 500 point do list and not a checklist.
People using a 500 point do list forget to set the DI because they don't know what to do, they need the do list and once the do list is done there is no check that it was done correctly i.e. there is no checklist just a procedure (do list) that is never checked.
A well designed and learned flow from memory is very good. One point leads to the next. A good example being the walk-round.
How many times have people been distracted during the walk-round and missed something that later turned out to be important (pitot cover)?
A good flow and then a proper checklist or some other appropriate cross-check (very short and only critical items) adds a layer of safety that is missing in both the flow alone or do list alone.
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Aviation CRM / Human Factors experts have done a good job of educating and changing habits in the medical industry. Two of the significant things they introduced were checklists and formal briefings in operating theatres. These simple things have saved lives.
Quite ironic to find that general aviation / flight training is perhaps less willing to make the same progress and embrace the same ideas and principles.