You ever get into one of those old cast iron drain lines with a million bends? My regular rod just binds up and I'm fighting it for an hour. The flexible one snakes right through... it's not about scrubbing power, it's about just getting the brush to the clog. Logan525 gets it, some jobs they're just the right tool. On a straight run I'd grab my solid rod every time, but for those tight old pipes, the bendy one saves my sanity.
Honestly I still think they're mostly a gimmick. A regular rod and a good brush gets into any corner just fine if you know what you're doing. Those bendy ones feel flimsy and don't really scrub with any power. I've worked on plenty of old homes and never needed one. It just seems like an extra tool to buy for no real reason.