The first video you posted above are geese. The much longer neck often gives it away.
Second video you posted are Pekin Ducks, from America.
First video below are common ducks, the most common type you see here in Europe. They don't seem to have a lot of trouble with their heads bobbing, just like the Pekin duck.
Many birds do have the bobbing, it is because their spine is all connected with muscle tissue from top to bottom. Movement of their feet travels all the way up to their heads.
Pigeons always have the bobbing, see bottom video.