Flashes have a purpose. And it's not to keep the horse's mouth closed!! They are there to stabilize the bit so that the rider's aids won't be confused by the bit moving, like then the horse chews the bit.
Drop nosebands are most commonly seen on stallions because they put pressure on the end of the nose bone and are a little harsher when the horse opens it's mouth and apparently that over-rides testosterone? They are also really useful for lunging! You can attach the line to both the noseband and the bit, so if the horse bolts the bit doesn't go through the mouth.
I don't think any of you have ridden many PSG/I1 horses. On some of them you NEED a double. At a certain point in the training the horses need re-enforcement up front. With some of them this point never comes because they are so sensitive. With others, like stallions with biiig necks, they eventually realize that they can undermine you with their necks. Then when they get hot in the tempis, your half halts stop going through and pretty soon you are doing a nice handgallop above the bit around the corners as a set up for your half pass/ three tempis which is NOT FUN in the middle of a test. So the double really comes in handy because you can just lift your hand(s) up sharply and all of a sudden your nice balanced horse is back :) Some horses don't need a double, some do. It's the same with some horses need spurs some don't, etc.
I think it's in the US the rule that doubles are not mandatory in FEI classes anymore, which is good, imo. Not in qualifiers or FEI sanctioned competitions though. They're still trying to push that through.