I have hunted turkeys for 25 years, so here's my two cents: It's a matter of pattern density.
Given the extra full chokes normally used when turkey hunting and #4 lead shot, there is an adequate pattern for the turkey to receive the requisite number of pellets in a vital spot out to any range you would reasonably shoot a turkey at. A quick trip to the patterning board with a turkey sillouette target will yield the proof.
With the ducks, you will probably open up to ic or mod chokes, and switch to #2 steel. With this combination, the pattern should hold together enough to cleanly kill ducks out to a reasonable range of 30-35 yds.
The geese are the problem, because you will likely move up to steel BB shot. Now, you have a problem because even using 3" 20 ga. shells, you will not be getting that many BB-size pellets in the payload to begin with. As the pattern spreads, you will quickly run out of pattern density, forcing you to either take closer shots, or jump up to a shell that holds more shot, such as 12ga or 10ga.
