I did the same idea with Rowdy. I didn't flick her onto the floor, but put her on her play gym and ignored her for a few minutes. Then we tried again. If she bit me, back on the play gym she went. I did have to clip her wings though so she didn't just fly right back. And with her wings clipped, she could not glide at all; she fell like a stone. So I could not have tried to lightly toss her to the floor without hurting her. Nandays are rather hefty for their size (they are made out of some unusually dense substance like cats

).
Our house is slightly large, and to get Loki to a play gym would require giving him undeserved attention. I personally find that it's better to deal with the situation immediately, and so he gets a "time out" on the floor (plus he views the play gym as fun time, so IMO, just like with a toddler, you don't put them somewhere fun when they're in trouble). It doesn't hurt him (and flicking is just the only description I can come up with, he's not literally flicked, he's never hit, he's never thrown, he's never hurt - EVER), he understands immediately that he's done something he's not supposed to and it really works. He is usually quite well behaved for a day or two afterwards

I say if it's not broke, don't fix it and this system for us certainly isn't broke! But for some birds, like Rowdy, that would also work because not being allowed to be with their person is certainly punishment enough!
I wasn't suggesting keeping them off your shoulder indefinitely. But, for example, when they are hyped up it might be a good idea to do so to avoid a bite. I've observed my bird and learned certain behaviors/circumstances that usually lead to biting. Now I'm able to avoid bites by avoiding certain circumstances. For example, I now know that Guava likes to scold me for leaving her to go pick up my girlfriend from work. Usually, she'll hop right to the top of her cage after being let out, and prance around for a few minutes with her chest poking out. If I were to attempt to have her step up at that point, she'd most likely bite. So I give her a few minutes to cool off, and she then willingly steps up. Or, I could keep attempting to have her step up and then have to punish her for biting. What I'm trying to say is, that in some cases it's simply easier on everyone to avoid it in the first place.
Not all birds have the same trigger over and over again. What can be fine one day, isn't the next. Loki is very Bipolar. While I agree that, much like with kids, you avoid putting them in the position in the first place, that's also not always possible. What sets my nephew off one day, might be perfectly fine the next. Which can be frustrating for both him and the grown ups caring for him! Yes, if you notice a pattern or that there are signs, certainly utilize those as tools. Unfortunately, not all of us have birds that are predictable.