because it is easier to fall ... I hit the brakes and went over the bar
Please do not be offended, and by all means keep on wearing a helmet if you want (after all it is safer, no denying that) but maybe there is room for improvement in your cycling? Those two things I quoted seem to indicate you haven't completely mastered cycling, or your bike isn't properly setup, or a combination of both. I see them for instance as well with foreigners who never owned a bycicle and then come to a country and are given one. For an experienced byciclist riding is usually a second nature, like walking, and falls don't happen more often then they do with walking. Note I'm talking 'normal' cycling here, not for instance downhill or bmx where not ever falling sometimes means you're not pushing yourself hard enough :]
Well, I have been riding bike well over 40 years and I do about 4000 km per year on bike, and I don't think I will master it any better in the future than I have so far. I don't fall often, but it happens more often than when walking and is definitely scarier. I mostly don't do "sports", I just commute.
And since bikes don't have ABS, I either have brakes that are not powerful enough, or I have brakes that throw me over the bar if I a mistake in a surprising situation (such as in the case I mentioned). Most falls I have are due to ice. Every winter morning is a decision: do I take the bike with studded tyres, or the one that is much lighter to ride? Sometimes I make the wrong assessment.
I still have a couple of years to go to reach that number of years, and doing roughly 3000km/year commuting. So I guess we just look at it differently then; I also ride bmx/dirt jumping, less in the last years because it can be quite harsh on the body, might be that it teaches you more control over a bike in general.
Ragarding the brakes: there are types which can bring you to a sudden halt if needed, but with a lever that still has lots of travel to allow for fine modulation. Usually the more expensive disc/rim brakes with oil instead of a steel cable are fine. Though I agree that if it's your instinctive reflex to completely squeeze the lever in a perilous situation it's either all or nothing.
Regarding ice: completely agree, even with proper equipment it's a struggle. And probably does lead to more falls then walking.
Please do not be offended, and by all means keep on wearing a helmet if you want (after all it is safer, no denying that) but maybe there is room for improvement in your cycling? Those two things I quoted seem to indicate you haven't completely mastered cycling, or your bike isn't properly setup, or a combination of both. I see them for instance as well with foreigners who never owned a bycicle and then come to a country and are given one. For an experienced byciclist riding is usually a second nature, like walking, and falls don't happen more often then they do with walking. Note I'm talking 'normal' cycling here, not for instance downhill or bmx where not ever falling sometimes means you're not pushing yourself hard enough :]