The only problems I have with a post cycle are that if one person disappears without warning it can throw a wrench into things, especially if that person is in a position where whatever their response would be can't be temporarily passed over, and it makes getting a character's two cents out a bit more tedious and less likely to be noticed in some situations because they're either writing long posts responding to everyone at once (which other players are likely to skim) or by the time it's their "turn" the response they wanted to make is obsolete in the chain of events.

Speaking of turns, will this post cycle have a certain order of initiative?