For me, the hand down -- on both marks and blinds -- is first and foremost a confirmation to the dog that they are looking in the right direction.
In addition, it creates a "barrier" for breaking. If you use it consistently, the dog understands that there is a sequence where it is not released to leave until the hand is down AND you have said its name. If you just say the name or back, the dog may (at some point) go on any breath or word it hears from you or someone else.
I line a dog up using Andy Attar's SHEA (I'm not sure if this is on his video, but it is in his workshop material) -- spine, head, eyes, attitude (in that order). Then my hand goes down on most things (except short memory birds) prior to sending.
There are things tha can be distracting. I feel that extra words and movements can be, so I use them carefully. I don't do a lot of "verbal coaching" with my dogs on the line. Nor will you generally see my feet move a lot, if at all, when I'm communicating to a dog on the line. I do think those things are distracting. And maybe with some dogs if you add a hand to all kinds of other movement, it could make things worse. I don't know... But for me, my movement is minimal to begin with. I want the dog to focus on the field and concentrate on where the birds are. And then I use my hand to tell them "that's right, that's where you should be going".
Of course, it's not always that simple, esp with a young dog just learning. But, in a nutshell, that's how and why I use a hand...
-K