I was pretty please I took a helmet on this trip.
When I flipped my boat and took a swim, my foot got caught in a shoulder strap of my pack. So, I had to go back under and free it. I was under for about 10 or 15 seconds during this process, and at the time, being delivered rapidly through Class III rapids.
While I was under, I hit my head on a rock hard enough to take a nice chunk out of my helmet (a carbon fiber Sweet Rooster low-profile ski helmet). After I freed myself from my boat, the current took me into a hole where the hydraulics slammed my shoulder, and I think, my head, into another rock.
Conclusion: Helmets are a good thing in rocky, shallow rivers because you may end up upside down for a bit. You could probably skip them in the Grand Canyon or other big, deep rivers, perhaps.
I'm looking for a WRSI-like helmet that's nice and light. There are not a lot. They seem to cost at least 1/4 lb more than the lighter climbing helmets out there.