Forgive me if I've got the wrong end of the stick here, but we seem to be confusing preflight checks with enroute/landing checks. Of course you can memorise the enroute/landing checks - let's face it, it doesn't take much to remember your FREDA checks - and most of them can, and often are, done perfectly safely. There's not much to commit to memory.
But when you're on the ground, why the big rush? Preflight checks on something like a PA38 are easy enough to remember, but why rely on your memory, especially as a low hours PPL student, when you have the time to go through it all with a checklist? Does it really take that much longer to run your finger down a list and action whatever needs actioning than doing it all from memory? I don't think so.