I actually use stirrups like these:
I think if an English stirrup fits right, the bulk of the ankle should prevent the foot from going thru. The one time I was tossed, I was dismounting with just my toe in the stirrup - further back than normal, as is my custom for a dismount - when my mare did a half-rear, 180 spin and bolt. I went flying. The next day, based on the bruising on my toe, I realized the one foot in the stirrup had slid in as far as it would go, then snapped out leaving a very distinct, sharp bruise across the side of my foot & toes.
If I switch to tapadero stirrups, it will really be to keep my stirrup from catching a branch. That happened the other day...no harm done to me or my horse, but it caught us both by surprise. That, and I love trying new tack - up to the limit of my budget, which usually happens early in the month!
I would also like to try stirrups with a wider base.