I restored a 1930s ladies bike (quite a long time ago now, it was found in a hedgerow in rural Cambridgeshire around 1999), that had a single rod brake. My view is that a bike equipped with them is only "dangerous" if it's ridden that way...
As some may recall, I fettled up an old 1940s Raleigh for my Aunt last year. That is the only rod-brake bike I have experience of (as an adult at least) and I thought the brakes were surprisingly effective. I'd be pretty confident riding round on it generally but would expect it to be as reluctant to stop in the wet as any other bike with chromed steel wheels.
Like any other vehicle, whether motorised or human-powered, if you use them within their limitations, they are fine. If you act like an idiot, you'll come unstuck.
If anything, I find rod brakes actually
more positive in their action than cable operated ones, and in dry conditions they are very effective - so long as your wheels are actually round that is! They're not great in the wet, but then nor are cable brakes on steel rims.
If caught out in the rain you adjust your speed and braking style accordingly; i.e. you keep drying the brakes off regularly as you ride rather than wait until you need them in an emergency.
Upright roadster bikes have a lot going for them in safety terms; the riding position gives a good view of what is going on around you, and they are generally not ridden at nutter speeds either, which means more time to react to any hazards.