I have NEW LC's, Pre and Post Techs, Super Speeds (40's and early Flares), and ball-end Old Types as well as a Fatip
Grande and Merkur 34G and 23C and even an ASD2. And have previously owned and sold a Muhle R89 and a Pre-War Canadian Fat Handle Tech. So at least some representations of rigid vs non-rigid types. I shave WTG,XTG, and ATG. These razors do shave differently (I like the Olds and NEWs), that's certain for me. But I have never experienced this flex and chatter that is spoken of. Like...never. Just sayin'. It seems weird to me, because one would think that the blade would be held against the top cap during the shaving stroke and couldn't possibly flick back and forth when it's gliding over softened whiskers and a surface lubricated by lather. I'm going to have to do a test of this and really compare two of my razors, like a post war Tech vs pre war or something else from the stable. Any suggestions from the razors I've mentioned?
Take a paper clip or something similar and carefully apply downward pressure on the blade edge towards the comb or safety bar. You'll quickly find the rigid designs.
If you have coarse and/or dense whiskers, rigidity does matter. If you dont have particularly dense or coarse whiskers, it may not matter for you. If not, consider yourself lucky lol.
I couldnt get a BBS finish over my trouble areas with my NEW LC and any blade I tried, but the SC wipes them right off with virtually any blade, Derby Extra included.
My post war Tech will get me to the same place, with 5-6 passes instead of 2-3 with the SC.