You know if you turn your bars in one direction, you fall in the other? Do that before you stop so you can always land on the unclipped foot. It's called countersteering. You already do it unconsciously while riding.

Please don't try to move both feet off the bike at the same time. To do that you'd have to hop, and hopping with unclipped feet will cause you to clip back in or slide off the pedal. I can't imagine how you came up with this idea. Do you do this on platform pedals? Stop doing that. Some cities offer free cycling skill classes. Maybe yours has one.

Regarding the "everyone falls issue", I fell twice when first starting with clipless pedals. I am a unicyclist, so balance is not one of my problems. Therefore no one needs to feel inadequate or smug about falling or not falling. I think it's pretty much luck.