I did catch one bit that I found interesting, and the reason it was so interesting was because it was "a thing."
I think that the main reason riders make the switch is that the double serves as a rite of passage. Third Level is no longer part of the lower levels. It's a big step towards the upper levels, the FEI, the Big Dogs, the Big Time. It's a Big Deal to move out of Second Level, and riders want to celebrate that success.
At least, that's how it looks from here.
We may need to move to a double bridle eventually, but I am going to hope not. Instead, I am going to work towards riding a Grand Prix test in a snaffle. Speedy's a hard worker, and he likes his job. He enjoys the challenges I present to him, and he tries his heart out for me. So far, the snaffle is working well.
Besides, snaffle bridles are a lot cheaper than a double. If nothing else, staying in a snaffle is a cost saver.