Our experience is the parrots who do that are instinctually moist food eaters or are birds with a need for wet food.. Eclectus and amazons are classic examples. It is not natural to force the birds onto a 75% or more pelleted diet simply because you have been told that is the easiest and best way to feed your birds.
Do a little test. Put five or six pellets into a small cup. Then with a teaspoon add equivalent amount of water and sit back and wait to see how long it takes to hydrate those dessicated pellets.
If a parrot without significant saliva is eating that dry diet, the same thing is going on in its crop—it has to drink that much water to moisten the foods given and it can take a long time depending on chewing and the kind of pellet. Most parrots do not by habit drink that much water. Especially dry land species like budgerigars, cockatiels, Australian cockatoos and parakeets, certain conures, etc. Therefore we are forcing our birds to eat a diet that is too dry for their evolved systems. Not good. It is also very dangerous when chicks in the nest end up with dry diet in a crop and not enough water to hydrate and digest it.
A parrot carrying his pellets to the water dish and dunking them is sending a message to its owners—I WANT WET FOODS!!
Give them more cooked and sprouted and soaked and raw foods.
Also pellets are not meant to be wetted and left standing. They become perfect medium for airborne bacteria and contact microbes to grow within. That soup you see after several hours can be a recipe for e coli or pseudomonas or whatever.