This resonates with the idea expressed in The Wisdom of Crowds - a group of people performs best if each of them brings their diverse perspectives (and biases) to the table. This happens only when people do their knowledge work independently.
If they confer - results end up being considerably worse, as diversity of perspectives gets superseded by "consensus" or most eloquently expressed opinions
Another potential source of convergence of perspectives is people using the same underlying sources of information
For the purposes of brainstorming - you probably don't want to have total independence, as you wan't to encourage Yes, and kind of interactions.
But you want to ensure that people don't block each other. Posting ideas to the common publicly visible place can be one mechanism that ensures this.