Plus you stand the best chance of "saving it" if you never let go.
This has worked a time or two for me, and believe me, after having fallen learning how to mountain bike a gazillion + 1 times, the only time I've actually hurt myself was when I let go...lesson learned again!
Our natural instinct is to try and stop our fall, our hip/side is so much stronger than our hand...
Never thought of holding onto the bars! Will try to remember that! but honestly, after that first fall, it's been very easy to clip in/ out and the pedals have helped me be a better rider. Now I know what people mean when they say different muscles engage when you're clipped in.
You're right about the injury...wrist bone fractures are very difficult to diagnose and can go untreated if there aren't any symptoms.
That surprises me to hear. From the very design of them, dirt/sand/grit are pushed out of the cleat when you push to engage. That's true at least for the Speedplay Frogs - which I use and love! (Can't comment on any other Speedplay models.) The Frogs are highly recommended by lots of TE members, because the (easily adjustable) degree of float and passive nature of the engagement is really easy on the knees.
ETA: I've caught up on the thread now and see a lot of others have pitched in in favour of Frogs!