I also think the black spots would help the vision of birds. I think, more black color in the iris would help absorbing unused light ways(for visualisation). It may serve a function of filter. Pale color or the iris may reflect light ways and they may interfere the shapeness of image formed in its brain (just make a guess).
The polymophism in black woodpecker may indicate that sharp vision is not as important as in bitterns (migrant vs non-imgrant?)...so the trait without the black spot could be retained.
I just try to make the story complete, because that is a very interesting topic!
Chun
