I have seen people get dragged but it was OFTEN because their foot was home in the stirrup AND SLIPPED FORWARD during a spook that then escalated...
I've come off once, using an English saddle. I was trying to dismount at the time, which meant my stirrup was at the ball of my foot. I normally use the home position, but use the ball of foot when dismounting. Mia had bolted. I had stopped her. But I tried to dismount without settling her, which was a bad idea. She did a small rear, spun 180 and leaped across a bunch of rocks. I must have come off at the start of the leap.
Only one foot was in the stirrup at the time. There was a very clear and distinct (and dark) bruise on my foot. Based on that, I know that during the excitement, my foot slid in until the heel of my cowboy boot stopped it. Then my foot and the stirrup did a brute force disconnect...
When things get exciting, your foot will go wherever it goes in a stirrup. That is part of why I always have worn cowboy boots, and make sure my stirrup is sized and shaped so my foot CANNOT go all the way thru. I also like my riding boots a looser than my 'go to church' boots. I want my feet to be able to slide out easily. I don't care if the horse runs off with my boot, provided I'm not still in it!
The home position was just about universal in the Old West.
It was taught by the US Cavalry. It is common in sports that involved aggressive riding - polo, steeplechase, cutting, roping, barrel racing. It is looked down on in dressage and WP - two sports that emphasize control, slower speeds and collection. VS Littauer, in the Showjumping Hall of Fame, recommended it. Harry Chamberlin, who largely wrote the Cavalry's manual on equitation, considered it critical for anything other than schooling an already trained horse.
It does not, in any way, prevent the heels from being down:
"Heels down" should come from one's weight flowing uninterrupted past the knees and in to the heels. Doing so means a sudden stop will drive you deeper into the saddle and stirrups rather than pitching you forward. It has nothing to do with the shape of the stirrup - I've done it in 2 bar English, 4 bar Australian and multiple western stirrups.
The home position is more commonly seen in western riding now than in English. Some say the folks I'm citing are out of date, that we "know more" than they did. I think the difference is that people used to spend more time riding outdoors, and now there is much more emphasis on riding in an arena.
I'm not suggesting anyone has to use the home position. Folks should use what works for them. But the home position was taught by people who did rough riding outdoors. It is still very common in western riding - maybe over 50%. It should not be ruled out, nor can I find any indication it is more dangerous. If it were more dangerous, folks riding rough would avoid it instead of adopting it....