Ok, now that I have a bit more time, I'll post why I do NOT like the checklist. (note this is mostly as advocatus diaboli.)
Skills like this should become rote. To the point where a checklist is completely redundant and superfluous.
I'd honestly probably be MORE worried if someone in my group started pulling out his little cue card before doing vertical work.
You use the example of a pre-flight checklist. I'm going on my general knowledge here and I welcome actual pilots to correct me.
In a case like an airplane, generally a pre-flight checklist is MUCH longer than what you may come up with here. So it's harder to do it "by rote".
Also, to an extent, the checklist is "the bible". It's done IN order as written w/o deviation unless allowed for and acknowledged. For vertical work, I think a) there's a bit more variability and b) there is no fully agreed on standard. Do I check my harness first, or do I check the rigging first? What is THE agreed on order we can all agree on. Your checklist may work very well for you, may seem foreign to me.
(now perhaps we SHOULD all have an agreed on order and resulting checklist, but I suspect cavers are far too ornery to ever agree on one ;-)
Finally, as written, I'd probably rewrite it to be more specific and "check/fail"
What's "On-rope!" really mean there?
Break that down;
Upper ascender correctly attached to rope, cam on rope and catch released: CHECK
Croll on rope, flat against chest, cam on rope and catch released: Check
Rather than saying "Is appropriate rope pad being used?" focus on the reason one is used; "Are all potential rub points properly rigged or protected?"
I've done many a drop where NO rope pad is being used. And perhaps the rub point is being avoided with a rebelay.
Brake Hand should never leave the rope. I disagree. At least as an absolute. If I've got a hardlock off on my descent device and I want to stop to take a few photos, I'll take my brake-hand off.
Oh, and "all carabiners locked", just to be clear, many times folks will have non-locking carabiners, so that's not always "true". (Though I'm being pedantic there, as I'll guess you really meant just locking carabiners
Hmm, thinking further, yeah, I'd expand upon what NZCaver said. Touch on stuff like approaching the drop. This is situational of course, some drops you'll rig in at the top and go, others you may need to crawl along a ledge for 40' before getting to the pit top itself.
Also I'm going to suggest you take a quick look at:
NCRC Student tests for some ideas. (Take a look at the SRT test.)
It's far from "complete" but may help.
Anyway, that's enough for now.