I guess I will have to just disagree a bit. I’ve also watched a lot of TOP riders who DO sit in Stadium and sit at moments that are NOT just oh crap moments. There are different kinds of sitting and even in some of the videos you posted I see riders sitting and setting up their horses.
I my case it is NOT to be behind to motion to send at all. It is to keep the rhythm and balance the same without using my reins. It is a way of slowing a horse down. BUT not all riders nor all horses should be ridden this way. I’ve helped some people riding my horses and because of what THAT rider did, told them to get up off the horse’s back and into two point…because they had a driving seat that was setting the horse off. Others were getting left behind. And after a time, that instruction might change to now they need to sit more.
It is just there is NOT a black and white rule on this. Bottoms should not be bouncing…that is a given…but there is time for riders to be in the tack more and a time not to be.
Denny Emmerson also just posted on this topic. Pointing out that you seat is an aid, and why would you not use all your aids? It is a more complicated question best suited to understanding the individual horse and rider and timing.
I will say that on my greener horses…I’m off their back more.