For approximately 25 yrs (Yes—I am _that_ old), 
I have refereed only non-anonymously
(as mentioned in [a previous MO question][1]).
It has not been uncommon that the authors of a paper I recommended with reservation—or, especially
those I rejected—to write me directly,
and we subsequently engage in an online (but off-journal) dialog to improve their paper,
often for another venue.
Almost uniformly these dialogs have been productively positive.
Easy for me to say, because of course I hold all the power strings.

Nevertheless, what Igor B. suggests seems to me would be a significant improvement 
on the current system.
My experience with the more one-sided communication I have experienced
predicts that it could work well.

  [1]: http://mathoverflow.net/questions/36596/refereeing-a-paper/36601#36601