To be honest I've never seen such a flange. I've seen some dirt bike rims with a bead area designed in such a way that you can run screws through it into the tire bead, I've seen the internal bead locks. I'd guess than any flange that extends outward around the bead would make mounting the tire next to impossible. I've heard of what you are talking about but never seen one.
About the fewest spokes I've ever seen on a wheel is 32, seems like there have been a few odd purpose wheels with 28. What can be misleading just looking at various spoke wheels is the different spoking patterns used. Typical of most Japanese bikes is the "cross 2" pattern, some Euro dirt bikes and Brit street bikes used "cross 4" pattern, and I'm sure there are others I haven't seen.
You know...now that I think about it...seems like I remember when bikes makers started touting "safety rims". Look at a mid 60's steel Honda rim...often very little height on the bead flange. I think in the later 60's or early 70's they started making rims with a taller bead flange, and they called these "safety rims" because the tire was less likely to come off the rim in a flat. I bet that's what you thinking of. To anyone under 50 years old the "safety" rims would probably be all they have ever seen.