Fixed gear, light single aircraft have very little on them which can kill you if you miss it - distraction from the job of flying is the big killer, so a mnemonic check is appropriate.
Complex light aircraft have wheels and more complicated fuel systems, single pilot distraction is still a problem, but a "do list", especially a mechanical one, is appropriate.
Two crew fast aircraft, where a mis-set flap or the like WILL kill you, and you have a second crew member to split the workload - checklists are mandatory.
Horses for courses.
I might also add - it depends upon how often you fly. I have always flown professionally, so the above applies to me - but it would be entirely appropriate to use a checklist if you fly as a hobby.