I don't have a strong opinion, and will go with whatever the majority decides, but I do have a lot of thoughts, so here they are:
I would like to see the option available to the individual to create a more complex plot, like while looking for wood Juni found an underground science lab and has to rescue something or other before continuing her wood search (assuming the scientists don't have wood). However...
I've been a part of a forum writing round robin that a bunch of submachine fans took part in, but unfortunately there where so many crazy teens involved who just wanted to make crazy stuff up and get the character almost killed at the end of their turn that it was obnoxious and overdrawn.
So, having an open option to make a more complex plot can only happen if you think you can trust the other game makers to not go crazy on you and leave you in a situation you don't have any interest continuing. Plus, if we keep switching the plot around, the level will just get pointless. I've been in DnD campaigns like that: so many side plots the main plot was lost.
But one thing to keep in mind is that no one should HAVE to contribute to plot development, but can simply add screens which carry the last plot point forward.
So, I like the idea of allowing side plots or adding complexity to the main plot, but the trouble is we have to be able to either trust each other to do a good job, or make tons of crazy rules and veto powers to make it work.