Checklists serve two purposes.
Firstly, they are used for confirmation that routine memory items have been completed at pre-determined stages of the operation.
Secondly, they direct courses of action for non-routine phases of flight in addition to confirming that memory items have been carried out as required.
In complex aircraft, and certainly in airline transport category aircraft, the checklists are numerous and often require action in combination with more than one checklist. These aircraft types also utilize two pilots normally, as well as possibly three autopilots. As such they enable checklists and "QRH's" to be utilized effectively as part of the operation.
I have to say that I personally find it quite disappointing to see the reliance that PPL trainees often place on their written checklists. In my opinion, basic training should be used to ingrain the use of mnemonics and memory items in the basic operating philosophy of simple aircraft types. Why?
Well, these basic operating mnemonics form the basic operating philosophy of almost every aircraft you are ever likely to fly. They should stay with you throughout your flying career. However you learn them, and whatever form they take, it is (with often minor modification) the same basic mnemonic that gets a 767 round the circuit, as it is a cessna 150 or a PA28. Instilling the confidence in a student during their basic training is (again in my opinion) something that will stay with them throughout their career, and will prevent the "emergency" that seems to form in their mind when the checklist slides under their seat, towards the back of the aircraft, or otherwise gets lost.
On the other side of that argument, is the fact that litigation and the need to train the use of checklist philosophy, presents its own realities that most flying instructors would be correct and quick to point out. Of course they are both very valid points. Checklists are a safety tool, and they are indeed the Standard Operating Procedure in any transport operation.
It therefore follows that in the real world the use of checklists must be taught, and their use properly followed in conjunction with both the aircraft manufacturers and the training organisations SOP's.
Neither method should therefore be exclusive of the other. However, the use of mnemonic memory based checks is still (I believe) fundamental to basic training, and a confidence builder that is not always being employed as often as it should be.