One thing nobody has mentioned yet is it is supposed to be a checklist, not a dolist. In theory, one does the necessary, then cleans up with the checklist to make sure nothing is missed. Following the finger down, or using a mnemonic, there's still a 'confirmation bias'. Probably still exists as a check, but perhaps less so.
I met this on final in an arrow, (re)checked the u/c - three greens, got to the end of the mnemonic, then realised that's only 2 greens. Turned out to be a bulb, but it provoked a go-around/full investigation/tower pass before finally putting it down. Still amazes me that I could 'see' three when there were only two.
For whatever it's worth, and PilotDAR's information, here's my approach - I'm not necessarily advocating, or defending. I'm a huge proponent of keeping eyes out of the window, this seems to work for me.
I hire, generally smallish SEP, including some retracts, and on the other end, decathlon/pitts. Recently mostly the latter, but when I was more regular I was mixing it a lot. Each aircraft was prepped by going through the flight manual thoroughly. I keep a small shirt pocket sized notebook, page per 'class' of aircraft - so something 'special' gets its own page. C172/PA28 get lumped into one page. An individual a/c with a significant mod/STC would get it's own page. Page gives approximate approach speeds, fuel peculiarities, salient points, anything different or important.
Mnemonics are generalised - one size fits all (e.g. prop pitch and U/c appear in the mnemonic whatever I'm flying, it's a memory prodder. Wheels? How are they, do I need to do anything with them.. etc. Pre-flight, review the page, and checklist depending on familiarity. In flight, pretty much entirely mnemonic - checklist is there if I need it.