Originally Posted by
PaulRivers
With road biking I haven't fallen over with flats on my bike since I was a small child and I'm in my 30's now.
With clipless I fell once at very low speed when I was first learning but I probably could have avoided that as well had I spent more time practicing before riding. Even there I have not fallen since then. (I've since gone back to flats but the reasons are unrelated to this topic).
If you can't ride a bike without periodically falling over onto the road I would suggest that perhaps biking is not for you, as it is fairly dangerous to fall onto blacktop. My uncle broke his hip doing it (not clipless).
But it's very uncommon for adults riding flat pedals to fall over on their bike. Not sure what else I could add.
The wisdom of youth

I'm in my 60s and have "fallen over" more times than I can count. It's not "periodically" but randomly and is usually caused by road conditions or, more specifically, surface conditions. Stuff happens. A bit of gravel on a corner, a patch of soft sand in a corner on a trail, a bit of water on a cross walk, a patch of ice, etc can all cause crashes...and have for me on many occasions. And your uncle breaking his hip on nonclipless pedals would indicate that crashing isn't related to clipless use.
On the other hand, if you never fall over, you'll never learn how to fall over. There is an art to crashing without it resulting in serious (or even moderate) injury. Platform pedals encourage behavior which results in more serious injury than clipless does. Most people ride platforms so that "they can catch themselves" when they fall. Doing that is about as dumb as "bracing for impact". Bits that are stuck out during a crash are bits that get bent at weird angles and get broken. Although I've crashed many times, I've only really "damaged" myself a few times. Most of the time, I come away with minor scrapes and bruises.
I'm not saying to rush right out and practice crashing but it's not a bad idea to learn how to crash by whatever means you can.