Yes, as I said holding onto the pommel is great for seat work on the longe. I can see how a grab strap would be useful on a really bad rooter on the forehand, but I’d want to go to systematic retraining that kind of horse :). As far as bucking or spooking or bolting, I would love if it could give me security, but I find that when real trouble happens my instinct is to sit up and back and do something like a one reined stop and my hands are nowhere near the grab strap.
When I learned to ride as a kid I recall that I held the Western saddle horn for a month for balance at the very start, but after that it stopped being an automatic reaction. I was taught to grab mane in two point and over fences in adult re-rider lessons and I will sometimes grab mane in a canter transition on the trails in a jump saddle. I now think that short cut in lessons actually gets in the way of learning a following release.
I do grab mane going up steep hills, always did that in preference to grabbing saddle horn as a kid, because it took pressure off saddle sliding backwards.
Anyhow it would be nice if there was something like a grab strap that would make me really secure on a horse that bucks but I feel like if I held on in front I’d just end up going over her head.
I can see that it might be useful learning to ride a horse with big gaits that wasn’t really giving you serious behavior problems.