...If your foot is all the way in, then if the horse spooks you have a very good chance of getting your foot caught in the stirrup...
Are you speaking from experience, or repeating what someone told you?
What I've noticed is that sports like polo, steeplechase, campdrafting, cutting etc are the ones where people ride with their foot deep in the stirrup. Julie Goodnight, in the link I posted earlier (although her link is now dead), said,
"Even though I teach students to ride with the stirrup on the ball of the foot, I tend to ride in the home position, particularly when riding Western. It's one of the rare times I will say "Do as I say, not as I do." For most riders, it is safest and most effective to ride with the stirrup on the ball of your foot.
For some disciplines, like cutting, working cow and even reining (my favorties!), riders like to have their foot all the way in the stirrup as an insurance policy against losing the stirrups. When the horse is moving dramatically and performing at high speed, it could be disastrous to lose a stirrup at the wrong moment. "
That was why I asked years ago if anyone knew of any statistics or studies. It seems odd that sports involving aggressive motion by the horse would favor the home position if that position was likely to result in your foot being caught. There are lots of old wives tales in riding, and I suspect this in one of them.
Mia used to spook daily. For about a year, as she was getting used to the desert, she would jump forward or sideways multiple times every ride. Since I didn't come off her, I don't know if riding in the home position would have been dangerous. My suspicion is that, if anything, it helped me stay on her. As an inexperienced rider, losing the stirrup when she was already scared would have been a bad thing for both of us.
Another campdraft picture (since I'm fond of Australian style saddles, and since Mia sometimes used to spook like that - glad she doesn't any more!):
I'm not asking anyone to start riding like that, but I'd love to see if anyone has any evidence it is bad.