I do understand that our Aikido is not mainstream but the wrist down approach is something that Shoji Nishio felt was a fundamental training flaw in Aikido
Thought I'd fill in a couple of things here.
First off, in my book it doesn't really matter whether your palm is up or down when you're actually doing a technique. Different situations call for different shapes etc. Rinkiouhen (or adapt on the fly) as Ark would say.
That being said the reason that the wrist, palm etc are turned down is because during training, you're initially trying to push the upper cross (read stretch across the sternum area) down, and keep it pushed down, pressurizing the tanden.
This eventually teaches the first vertical rotation that occurs within the body, (and more importantly in the tanden) where the front drops, gets pulled down, while pressure rises up the backside. (This is a physical skill, not something that you're supposed to fantasize about)
For "#$#"s and giggles, lets take a simplistic model.
Assuming the arms are connected through the upper cross, let's simplify the issue and look at the arms like they're a rubber hose. This means it has an elastic nature, and if pulled in various directions, will desire to come back to it's original shape.
If you rotate the hose sagitally, so that it turns down the front and up the back (while holding the ends in place) use start to get a very basic form of torque to develop. The direction of the torque also happens to...do something to the arms, but I think I'll let some figure it out for themselves. But it's that local torque (and I want to be clear that the torque I'm describing above is more "local" than whole body) that joins itself naturally to executing the kind of techs that Chris put up.
The same kind of principle is taken to a deeper level, and starts to involve the tanden etc, becoming more whole body as you progress.
That being said, my main point being there's a logic and rhyme to a lot of the "shapes" used, and most of it I think has little do with whether you're holding a weapon or not etc. (That's not meant as a slant towards you William, I'm just trying to illustrate a point).