/Disclaimer I've only read the first few pages and am completely new to the forums!
I think what is being left out in this discussion is when and why one would surpress rather than just kill. We all 'know' supression from reality, but let's face it, TBS is not always a good model. In most situations you would just go for the kill, unless surpression is so overpowered you always want to use it first, if you get my meaning.
The main use I can see is a position held by the aliens (or yourself) that is extremely well fortified in the sense of reaction shots and limited flanking possibillities. This is a situation where it is hard to hit the aliens themselves, but where surpression can lead you to tactically new situations. That leads me to the conclusion that surpression should mostly impair reaction shots and accuracy, and nothing else.
I assume reaction fire works the same as in X-COM, so a reduced reaction also means that an alien that runs from cover while being surpressed in its own turn, will more easily trigger reaction shot from your soldiers. This will effectively pin them down, while still giving them the option of running like hell. It also 'simulates' reduced awareness when being pinned down, making a flanking manouever possible that at first might've been too dangerous. Finally, by reducing aim you simulate the fact that they will be unable to take careful shots, although you could also just 'disable' aimed fire when pinned down or something similar.
I just think this makes more sense from a gameplay point of view, more so than affecting AP (which sounds horrible to me) or just aim (too ineffective).
My 2 cents
[edit] I see now that the poster above me says something similar
