When you strip the fly in, you aren't using the reel like you would with a baitcast or spinning setup. You gotta put the line somewhere! lol
First off she was most likely fishing for trout which are extremely spooky. I've had to crawl up to some pools when the water is gin clear in order not to spook fish (Even when I do, I see the odd monster spec swim out of the riffle and into the wood). Also, unless you are rollcasting, you need to make a few false casts in order to get the right amount of line out. False casts over the water does spook the fish, she was most likely trying to avoid that.
People do, but it's a lot more fun by using your hand
Depending on what you are fishing for, you cannot present the bait any better then with a flyrod.. It's also a purist sport, the bare minimums..
You should try it, you might be able to answer that all by yourself
BTW, I'm a complete rube at flyfishing, but it's a fun way to spend the day.