As opalescent said, primary relationships are important for some polyamorists, not so much for others.
Re: doors ... I think of them as symbols of respect (for each other's personal space and privacy). Communication is indeed important, and the heavy discussions should happen when everyone is at a good stopping place which generally means scheduling a specific time beforehand (a time everyone agrees to) for a sit-down. This way people will know ahead of time when they'll be opening their doors and emerging for the discussion that needs to happen.
If something suddenly comes up that can't wait and has to be talked about right away, I think of it as a gesture of respect to knock on the person's door and let them be the ones to open it or perhaps ask for a few minutes beforehand.
A doorless set-up would be great for a group of people who were very easy-going, open to talk at any time and under any circumstances, and not in need of any kind of secure privacy. In a household with children, doors help reinforce (in a tactile way) that there are certain spaces that are sacred to the individuals in them at any one given time.
I think there's a few commune-style polyamorists, and a whole lot of regular-old colonial-American style polyamorists. The doorless ideal would appeal to a very small slice of the poly population.
Love means never having to say, "Put down that meat cleaver!"