Talking with people whose stubble I have seen, I have come to the following conclusions.
1. Fine hair with smooth skin (or a razor with no significant exposure): The blade rigidity just doesn't matter at all.
2. Skin irregularities like acne: A rigid blade helps a lot. This seemed backwards when I was told this, but it makes sense in that if the blade snags on something enough to flex the blade, it will flex toward the skin regardless of whether the razor is being held steep or shallow (albeit less so with shallow).
3. Coarse beards: Rigidity matters a great bit, but I am starting to think a blade that is allowed to flex some is better for comfort and maybe even closeness as long as it does not flex so much that it chatters. Too stiff is not ideal, but too loose is really bad for those with coarse hair.
In another thread, I was (I think incorrectly) talking about damping of the blade. While I was close to something, there is nothing other than the skin that really dampens anything. . . . and I just knew I was missing something. Andrew at Paradigm has convinced me (gently and offline) that it is more of a harmonics or blade resonance issue:
The blade in any razor will have a set, undamped natural frequency. The impact of the stubble on the blade (what we call feedback) is more or less noise with a random impact frequency--but the frequency still has a range. I think the range is roughly in the 100-200 Hz range depending on how fast I rub something like a stiff metal ruler over my face and listen for the range of pitches. It is definitely not a single pitch. If the razor is stiff enough that its natural frequency is above that of the range of stubble noise, the blade won't chatter or experience resonance with the stubble. This is mainly true for coarse hair in that fine hair won't drive the deflection enough to matter much I am guessing. I wouldn't know--I have coarse hair, and it matters a great deal.
To find blade frequency in the razor, I use an old blade in the razor and listen for the pitch when I flick it (and then sing the pitch into a vocal pitch app). My son actually runs a rosined cello bow hair over the tip of the blade (after threading inside the safety bar) to drive the blade with the bow hair like he would a cello string to listen for the pitch of the blade (and then he plays the pitch on his cello). We get the same results--it is a definite pitch, unlike "stubble noise". The more rigid blades have a higher pitch or higher frequency. A Gen2 CGL3 has a pitch of around 220 Hz--I think it is about perfect (just above "stubble noise" frequency giving some blade flex but not yielding resonating chatter) and I think it's why people find it (the GEN2) so smooth compared to the GEN1 even though they have the same shave plane geometry. . . I just wish the safety bar design were more like a Paradigm. My Diamondback was around 350 Hz. Very rigid razors will be higher. The added ability for the blade to flex (while staying well away from resonance) is why I think the Diamondback is comparing favorably against very rigid, very high-end razors. . . . although I think it has room for just a little more flex without resonating.
I know my theories on this are in flux, but this is where I currently am, and I don't have a gnawing feeling like I am missing something (like I did with damping). Now that school is out, I may have my son use his cello bow hair to find pitches of many of my razors. . . . .if anyone was interested??