I haven't gone clipless yet -- but I read this thread with interest and two comments jumped out at me.
One -- we've learned to do many things that are much more difficult. (Good point!)
Two -- it's the unexpected that we aren't ready for.
My two falls on my bike in the first few weeks were with platform pedals. They were both because I wasn't accustomed to handbrakes and stopping/dismounting. Oh, I thought I was because I had no probs at all when I was approaching a stop sign or some other reason I needed to stop.
But it wasn't instinct yet, and so when something unexpected happened, both times my first instinct was to use coaster brakes (oops) and I also simply hadn't practiced enough.
So my suggestion to you (even though I haven't done it myself) is to just practice more -- clipping, unclipping, getting on and off. And (as others advised me) practice stopping and unclipping quickly in "emergency mode," like going pretty fast and then having to brake and dismount.
I just got toe grips and am hoping I don't fall two more times, and then later when I try to go clipless. But if I do -- eh, I've fallen and gotten some pretty nasty bruising, but it healed. ;)