Hmm, What kind of bike at what kind of speed on what kind of surface?

It's entirely possible to ride a bike in a way that actually doesn't require a helmet. It's VERY boring :-P , but nevertheless practical and doable.

Probably about 15 to 20 mph. Once on a country road going down a hill in a bend; I slipped on loose gravel and had to replace my helmet. The second time, about the same speed but on a country bike path (flat land, next to a canal). I slipped on a large wet stone embedded in the path and again had to replace my helmet.

I've fallen a few other times besides those two, but those are the worst two and I think without a helmet I would have been seriously injured if not dead.

I ride without a helmet and essentially never go beyond about 12 MPH, and more often in the 6-8 range. I take sidewalks generously, stay out of mixed traffic, and frequently stay in low gear, and this is still over twice as fast as an average walking pace.

I think it's all relative to how much you're approaching it as "road cycling" vs "urban commuting". If you keep the seat high, lean forward, and pedal near your limits, you definitely need protection even if the road is empty. But if you're going at a pace and a posture that lets you stomp your foot down easily, the dangers come down to total loss of control(e.g. downhill, failing brakes) and unpredictable traffic.

The biggest danger with electric mobility going forward lies in blurring of the distinctions. When they're brought up to highway speeds, what you have is an underbuilt motorcycle with no safety features or licensing requirements.

Don't forget wet leaves. I was riding my bike well after it had rained, and most of the path was dry, but there was a shady spot under a tree that still was wet and I basically lost all traction on it. Only time I ever "used" my helmet.

Or half buried campfire rings (aka a repurposed truck wheel rim) hidden by the grass on the side of a hill.. I think I must have done about two flips in the air after hitting that. At least in that case I don't think I hit my head hard, I landed in the same grass which cushioned my landing, but if there had been something else hidden in the grass I might have lost more than just a bicycle wheel.