The biggest reason I advocate flooding on a budgie is because I think many budgie owners aren't taking the time to train through positive reinforcement. As you said, on a budgie you can get away with it while a larger parrot could bite so hard you couldn't stand it. But this is not all of it. As you know I had experience with a budgie. I noticed that their reaction to flooding is somewhat different than even a small parrot like a Senegal Parrot. Essentially, they are pretty dumb and forgiving. They have a very fast metabolism and go crazy for millet spray (Truman could never get so excited over food) so it seems to outweigh the grabbing for them.
By the way, notice that I never recommend pure flooding. I always suggest coupling it with positive and negative reinforcements. Now that Kili is tame, you can see me use flooding on her as well in this combination as I did for wearing the harness. Essentially systematic desensitization requires small but progressive amounts of flooding. You can get away with doing this off the bat to tame a budgie but it is too harmful to the owners (and also the parrot catches on that the owner will be forceful and hate the owner) on larger parrots. I don't know what it is but larger parrots seem much more prone at developing phobias than the little ones.







